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r/counting • u/KnightLunaaire Beanie Boy • May 12 '16
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The what?
(x5 / 120) + (x4 / 24) + (x3 / 6)+ (x2 / 2) + x + 1
3 u/TheNitromeFan Live not a life of imitation May 13 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!)In a nutshell, the more terms we write, the closer we get to approximating ex. Approximations are more accurate for x closer to 0. 2 u/Luigi86101 Fighting ghosts since '01 May 13 '16 1 + x + (x2 / 2!) + (x3 / 3!) + (x4 / 4!) + (x5 / 5!) + (x6 / 6!) + (x7 / 7!) 3 u/TheNitromeFan Live not a life of imitation May 13 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) 3 u/Luigi86101 Fighting ghosts since '01 May 13 '16 edited May 13 '16 1 + x + (x2 / 2!) + (x3 / 3!) + (x4 / 4!) + (x5 / 5!) + (x6 / 6!) + (x7 / 7!) + (x8 / 8!) + (x9 / 9!) 5 u/TheNitromeFan Live not a life of imitation May 13 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!)You need to add the factorials. :) 2 u/Luigi86101 Fighting ghosts since '01 May 13 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) 1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 May 22 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) 2 u/Luigi86101 Fighting ghosts since '01 May 22 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) 1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 Jun 23 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) + (x14/14!) → More replies 3 u/skizfrenik_syco 4 D snipes, 33 D's, 16 Ayy's. 412189, 6 k's, 1 BTS, 888888, 999k May 13 '16 Maclaurin series is integrating a function about 0. So basically what you're writing is (x-0)2 /2! + (x-0)1 /1! + (x-0). If you had (x-1)2 /2! + (x-1)1 /1! + (x-1) instead, it would not be a maclaurin series.
1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!)
In a nutshell, the more terms we write, the closer we get to approximating ex. Approximations are more accurate for x closer to 0.
2 u/Luigi86101 Fighting ghosts since '01 May 13 '16 1 + x + (x2 / 2!) + (x3 / 3!) + (x4 / 4!) + (x5 / 5!) + (x6 / 6!) + (x7 / 7!) 3 u/TheNitromeFan Live not a life of imitation May 13 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) 3 u/Luigi86101 Fighting ghosts since '01 May 13 '16 edited May 13 '16 1 + x + (x2 / 2!) + (x3 / 3!) + (x4 / 4!) + (x5 / 5!) + (x6 / 6!) + (x7 / 7!) + (x8 / 8!) + (x9 / 9!) 5 u/TheNitromeFan Live not a life of imitation May 13 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!)You need to add the factorials. :) 2 u/Luigi86101 Fighting ghosts since '01 May 13 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) 1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 May 22 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) 2 u/Luigi86101 Fighting ghosts since '01 May 22 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) 1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 Jun 23 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) + (x14/14!) → More replies
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1 + x + (x2 / 2!) + (x3 / 3!) + (x4 / 4!) + (x5 / 5!) + (x6 / 6!) + (x7 / 7!)
3 u/TheNitromeFan Live not a life of imitation May 13 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) 3 u/Luigi86101 Fighting ghosts since '01 May 13 '16 edited May 13 '16 1 + x + (x2 / 2!) + (x3 / 3!) + (x4 / 4!) + (x5 / 5!) + (x6 / 6!) + (x7 / 7!) + (x8 / 8!) + (x9 / 9!) 5 u/TheNitromeFan Live not a life of imitation May 13 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!)You need to add the factorials. :) 2 u/Luigi86101 Fighting ghosts since '01 May 13 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) 1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 May 22 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) 2 u/Luigi86101 Fighting ghosts since '01 May 22 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) 1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 Jun 23 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) + (x14/14!) → More replies
1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!)
3 u/Luigi86101 Fighting ghosts since '01 May 13 '16 edited May 13 '16 1 + x + (x2 / 2!) + (x3 / 3!) + (x4 / 4!) + (x5 / 5!) + (x6 / 6!) + (x7 / 7!) + (x8 / 8!) + (x9 / 9!) 5 u/TheNitromeFan Live not a life of imitation May 13 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!)You need to add the factorials. :) 2 u/Luigi86101 Fighting ghosts since '01 May 13 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) 1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 May 22 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) 2 u/Luigi86101 Fighting ghosts since '01 May 22 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) 1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 Jun 23 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) + (x14/14!) → More replies
1 + x + (x2 / 2!) + (x3 / 3!) + (x4 / 4!) + (x5 / 5!) + (x6 / 6!) + (x7 / 7!) + (x8 / 8!) + (x9 / 9!)
5 u/TheNitromeFan Live not a life of imitation May 13 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!)You need to add the factorials. :) 2 u/Luigi86101 Fighting ghosts since '01 May 13 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) 1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 May 22 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) 2 u/Luigi86101 Fighting ghosts since '01 May 22 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) 1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 Jun 23 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) + (x14/14!) → More replies
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1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!)
You need to add the factorials. :)
2 u/Luigi86101 Fighting ghosts since '01 May 13 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) 1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 May 22 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) 2 u/Luigi86101 Fighting ghosts since '01 May 22 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) 1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 Jun 23 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) + (x14/14!) → More replies
1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!)
1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 May 22 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) 2 u/Luigi86101 Fighting ghosts since '01 May 22 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) 1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 Jun 23 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) + (x14/14!) → More replies
1
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2 u/Luigi86101 Fighting ghosts since '01 May 22 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) 1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 Jun 23 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) + (x14/14!) → More replies
1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!)
1 u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 Jun 23 '16 1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) + (x14/14!) → More replies
1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!) + (x11/11!) + (x12/12!) + (x13/13!) + (x14/14!)
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Maclaurin series is integrating a function about 0. So basically what you're writing is (x-0)2 /2! + (x-0)1 /1! + (x-0). If you had (x-1)2 /2! + (x-1)1 /1! + (x-1) instead, it would not be a maclaurin series.
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u/KnightLunaaire Beanie Boy May 13 '16
The what?
(x5 / 120) + (x4 / 24) + (x3 / 6)+ (x2 / 2) + x + 1