What is the fifth term of the expansion of (a + b)^8?
I get how to do everything up to the point where you need to find the coefficient. Somehow I missed this in my 13+ years of mathematical training, and I can't find an internet source that adequately explains how to solve this for the coefficient! Please help! Thank you! I'll pick a best answer TODAY!!!!!
2007-08-19 04:44:07 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
its 8C5 = 8!/(5! 3!) = 8x7x6 / (1x2x3) = 56
2007-08-19 04:56:38 · answer #1 · answered by vlee1225 6 · 0⤊ 1⤋
Take a loot at Pascal's triangle:
http://en.wikipedia.org/wiki/Pascal%27s_triangle
If you have
(a+b)^n
then coefficients on the terms of the expansion are the values in the (n+1)th row of Pascal's triangle. So, the coefficients of the terms for (a+b)^8 are
1, 8, 28, 56, 70, 56, 28, 8, 1
but only if the terms are ordered like this:
a^8, a^7*b, a^6*b^2, a^5*b^3, a^4*b^4, a^3*b^5, a^2*b^6, a*b^7, b^8
2007-08-19 11:57:26 · answer #2 · answered by lithiumdeuteride 7 · 1⤊ 0⤋
Check out Pascal's triangle for the coefficients.
I'm not clear why you need the fifth term.
2007-08-19 11:57:45 · answer #3 · answered by iceman 2 · 1⤊ 0⤋
The binomium of Newton says that
(a+b)^n = sum(k=0,k=n) n!/k!(n-k)! a^k b^(n-k)
So if n=8 and k=4 (fifth term) we have 8!/4!4! a^4 b^4
or (8x7x6x5/4x3x2x1) a^4 b^4 = 70 a^4 b^4
2007-08-19 11:57:40 · answer #4 · answered by ?????? 7 · 1⤊ 0⤋
8C4 a^4 * b^4
-----------
Ideas: You count from 0.
2007-08-19 11:51:35 · answer #5 · answered by sahsjing 7 · 1⤊ 0⤋