Question

Cho S=1/1x3+1/2x4+1/3x5+..............+1/97x99+1/98x100

So sánh S với 1

Answer 1

\(S=\frac{1}{1.3}+\frac{1}{2.4}+\frac{1}{3.5}+...+\frac{1}{97.99}+\frac{1}{98.100}\)

\(S< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{97.98}+\frac{1}{98.99}\)

\(S< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{97}-\frac{1}{98}+\frac{1}{98}-\frac{1}{99}\)

\(S< 1-\frac{1}{99}< 1\)

=> S < 1

Answer 2

Cảm ơn bạn nhé