Câu hỏi của •Iċε ℌαċкεɾ (Čїεℓ*)•

Question

$CMR:\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}< 2$

Nguyễn Linh Chi · Accepted Answer

$\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}$

$< 1+\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}$

$=1+\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}$

$=2-\frac{1}{50}< 2$

Câu trả lời:

$\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}$

$< 1+\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}$

$=1+\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}$

$=2-\frac{1}{50}< 2$

Nguyễn Ngọc Anh Minh · Answer

Vế trái =VT

$VT< 1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}$

$VT< 1+\frac{2-1}{1x2}+\frac{3-2}{2x3}+\frac{4-3}{3x4}+...+\frac{50-49}{49x50}$

$VT< 1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}=2-\frac{1}{50}< 2$

Câu trả lời:

Vế trái =VT

$VT< 1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}$

$VT< 1+\frac{2-1}{1x2}+\frac{3-2}{2x3}+\frac{4-3}{3x4}+...+\frac{50-49}{49x50}$

$VT< 1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}=2-\frac{1}{50}< 2$