Question

find the fourth term of (x+5)^7

Answer 1

Use the binomial theorem:
\[(a+b)^n=\sum_{k=0}^n\binom nk a^kb^{n-k}\]
Here, \(n=7,~a=x,~b=5\). The fourth term occurs when \(k=3\), so it's
\[\binom73 x^35^{7-3}\]