Question

giúp em với em cảm ơn nhiềuuuuu

Answer 1

Do n lẻ, đặt \(n=2m+1\)

\(\Rightarrow S=C_{2m+1}^1+C_{2m+1}^2+...+C_{2m+1}^m\)

Áp dụng đẳng thức: \(C_n^k=C_n^{n-k}\)

\(\Rightarrow S=C_{2m+1}^{2m}+C_{2m+1}^{2m-1}+...+C_{2m+1}^{m+1}\)

\(\Rightarrow2S=S+S=C_{2m+1}^1+C_{2m+1}^2+...+C_{2m+1}^{2m}\)

\(=C_{2m+1}^0+C_{2m+1}^1+...+C_{2m+1}^{2m+1}-\left(C_{2m+1}^0+C_{2m+1}^{2m+1}\right)\)

\(=2^{2m+1}-2\)

\(\Rightarrow S=2^{2m}-1\) luôn lẻ (đpcm)