Question

S=3/4 + 8/9 + 15/16+ 24/25 +. .......+2499/2500 CMR: S ko phải là só tự nhien

Answer 1

Do S = \(\frac{3}{4}+\frac{8}{9}+...+\frac{2499}{2500}\)

\(\Rightarrow\)S = \(\left(1-\frac{1}{2^2}\right)+\left(1-\frac{1}{3^2}\right)+...+\left(1-\frac{1}{50^2}\right)\)

\(\Rightarrow\)S=(1+1+1+...+1) - \(\left(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}\right)\)

\(\Rightarrow\)S=49-\(\left(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}\right)\)

Dễ thấy:\(\left(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}\right)\)không phải là số tự nhiên

\(\Rightarrow\)S\(\notin N\)