Question

CMR:  1/2² + 1/3² +1/4²+ 1/5² +1/6² +...+1/100²<3/4

GIÚP TỚ VỚI.THANK YOU

Answer 1

đặt biểu thức trên là A

A < 1/2² + 1/2.3 + 1/3.4 + 1/4.5 + ... + 1/99.100

A < 1/4 + 1/2 - 1/100 < 3/4

vậy A < 3/4

Answer 2

Đặt S=1/2²+1/3²+1/4²+...+1/100²

Vì 1/3²=1/3.3<1/2.3

1/4²=1/4.4<1/3.4

Suy ra 1/2²+1/3²+1/4²+...+1/100²<1/2²+1/2.3+1/3.4+...+1/99.100

S<1/2²+1/2-1/3+1/3-1/4+...+1/99-1/100

S<1/4+1/2-1/100

S<3/4-1/100<3/4

Suy ra S<3/4(ĐPCM)