Question

Cho B=1/2^2+1/3^2+...+1/50^2 c/m B<3/4

Answer 1

Lời giải:

Ta có: 

\(\frac{1}{3^2}=\frac{1}{3.3}< \frac{1}{2.3}\)

..........

\(\frac{1}{50^2}< \frac{1}{49.50}\)

Cộng theo vế:

\(B< \frac{1}{2^2}+\frac{1}{2.3}+...+\frac{1}{49.50}=\frac{1}{4}+\frac{3-2}{2.3}+....+\frac{50-49}{49.50}=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{49}-\frac{1}{50}\)

\(=\frac{1}{4}+\frac{1}{2}-\frac{1}{50}< \frac{3}{4}\)

Ta có đpcm