Question

1)CMR

a) 1/2^2 +1/3^2+......+1/2018^2 < 1

b) 1/2^2 +1/4^2+1/6^2+......+1/2018^2<1/2

c)E=1/2^2+1/3^2+....+1/100^2<3/4

Giúp mình với m đang cần gấp lắm 😱😱😱

Answer 1

a)Ta có: 2²>1.2⇒\(\frac{1}{2^2}< \frac{1}{1.2}\)

3²>2.3⇒\(\frac{1}{3^2}< \frac{1}{2.3}\)

... 100²>99.100 ⇒ \(\frac{1}{100^2}< \frac{1}{99.100}\)

VT < \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)\(=1-\frac{1}{100}< 1\)(ĐPCM)