Chứng minh các bài toán sau bằng phương pháp quy nạp:1. a) $1^{2}-2^{2}+3^{2}-4^{2}+...+(-1)^{n+1}n^{2}=(-1)^{n+1}\frac{n(n+1)}{2}$
b) $1.2.3...p+2.3...p(p+1)+...+n(n+1)...(n+p-1)=\frac{n(n+1)...(n+p)}{p+1}$
c) $\frac{a+1}{2}+\frac{a+3}{4}+\frac{a+7}{8}+...+\frac{a+2^{n}-1}{2^{n}}=\frac{(a-1)(2^{n}-1)}{2^{n}}+n$
2. a) $2^{n+2}3^{n}+5n-4$ chia hết cho 25.
b) $5^{2n+1}+2^{n+4}+2^{n+1}$ chia hết cho 23.