Yahoo Answers: Answers and Comments for How do you solve (x+1)^100? [Mathematics]
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From ?
enUS
Sat, 10 Oct 2009 20:54:45 +0000
3
Yahoo Answers: Answers and Comments for How do you solve (x+1)^100? [Mathematics]
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From steve112285: If you want to expand it, you can write it as ...
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Sun, 11 Oct 2009 04:13:47 +0000
If you want to expand it, you can write it as Sum[(100,k) x^k, k, 0, 100], a sum from 0 to 100 over the index k. The coefficients (100,k) are called binomial coefficients, and they have the value 100!/[k! (100k)!] (read about factorials if you don't know this notation). Some of the terms look like:
(x+1)^100 =
(100,100) x^100 + (100,99) x^99 + (100,98) x^98 + ... + (100,1) x + (100,0) =
100!/[100! (100100)!] x^100 + 100!/[99! (10099)!] x^99 + 100!/[98! (10098)!] x^98 + .. + 100!/[1! (1001)!] x + 100!/[0! (1000)!] =
100!/[100! 0!] x^100 + 100!/[99! 1!] x^99 + 100!/[98! 2!] x^98 + ... + 100!/[1! 99!] x + 100!/[0! 100!] =
1/0! x^100 + 100/1! x^99 + 100*99/2! x^98 + ... + 100/1! x + 1/0! =
x^100 + 100 x^99 + 4950 x^98 + ... + 100 x + 1

From Jason B.: USe Pascal's Triangle
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Sun, 11 Oct 2009 04:02:33 +0000
USe Pascal's Triangle

From triestobehelpful: (x+1)^100 equals what? Or do you mean if x = 2...
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Sun, 11 Oct 2009 03:59:51 +0000
(x+1)^100 equals what? Or do you mean if x = 2 then your term equals 3^100?

From Anonymous: use binomial theorem.
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Sun, 11 Oct 2009 03:59:09 +0000
use binomial theorem.

From Juan T: Use a computer it may take a while it can be s...
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Sun, 11 Oct 2009 03:57:24 +0000
Use a computer it may take a while it can be solved usiong series approximation!

From Anonymous: What is x equal?
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Sun, 11 Oct 2009 04:02:16 +0000
What is x equal?