Question

доказать что (1) равно (2)...​

Answer 1

$2-\frac{k+2}{2^{k}}+\frac{k+1}{2^{k+1}}=2+\frac{-2\cdot (k+2)+(k+1)}{2^{k+1}}=2+\frac{-2k-4+k+1}{2^{k+1}}=2+\frac{-k-3}{2^{k+1}}=\\\\=2-\frac{k+3}{2^{k+1}}\\\\\\\star \; \; 2^{k+1}=2^{k}\cdot 2\; \; \star$