Question

..FOLLOWING EXPANSION,FIND THE TERM STATED.
(1+X)^10, 5TH TERM

Answer 1

@Abmon98

Answer 2

\[\left(\begin{matrix}10 \\ 0\end{matrix}\right)1^{10}+\left(\begin{matrix}10 \\ 1\end{matrix}\right)(1^{9}*x^1)+\left(\begin{matrix}10 \\ 2\end{matrix}\right)(1^8*x^2)+\left(\begin{matrix}10 \\ 3\end{matrix}\right)(1^7*x^3)+\left(\begin{matrix}10 \\ 4\end{matrix}\right)(1^6*x^4)\]
\[(a+b)^n=\sum_{k}^{n}\left(\begin{matrix}n \\ k\end{matrix}\right)(a ^{n-k}*b^k)\]\[\left(\begin{matrix}n \\ k\end{matrix}\right)=n!/k!(n-k)!\]
\[\left(\begin{matrix}10 \\ 0\end{matrix}\right)=10!/(10-0)!0!=1\]
\[\left(\begin{matrix}10 \\ 1\end{matrix}\right)=10!/(10-1)!1!=10\]
\[\left(\begin{matrix}10 \\ 2\end{matrix}\right)=10!/(10-2)!2!=45\]
\[\left(\begin{matrix}10 \\ 3\end{matrix}\right)=10!/(10-3)!3!=120\]
\[\left(\begin{matrix}10 \\ 4\end{matrix}\right)=10!/(10-4)!4!=210\]

Answer 3

i think you can now continue till the term x^5

Answer 4

But the given answer is 210x^4
@Abmon98

Answer 5

\[\left(\begin{matrix}10 \\ 5\end{matrix}\right)(1^5*x^5)+\left(\begin{matrix}10 \\ 6\end{matrix}\right)(1^4*x^6)+\left(\begin{matrix}10 \\ 7\end{matrix}\right)(1^3*x^7)+\left(\begin{matrix}10 \\ 8\end{matrix}\right)(1^2*x^8)+\left(\begin{matrix}10 \\ 9\end{matrix}\right)(1*x^9)+x ^{10}\]

Answer 6

Count from 1^10 5 terms

Answer 7

you will find out that the answer is 210x^4

Answer 8

Okay
Got it
Thanks @Abmon98

Answer 9

your welcome :')