Question

Cho C =3/4 + 8/9 + 15/16 +. . . + 9999/10000

CMR C >98

Answer 1

C = ( 1 - 1/4 ) + ( 1  - 1/9 ) + ( 1 - 1/16 ) + .. .+ ( 1 - 1/10000 )

C = 1 + 1 + ... + 1 - ( 1/4 + 1/9 + 1/16 + ... + 1/10000 )

C = 1 + 1 + 1 +... + 1 - ( 1/2² + 1/3² + .. + 1/100² )

C = 99 - ( 1/2² + 1/3² + ... + 1/100² ) 

Mà 1/2² + 1/3² + ... + 1/100² < 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/99.100 = 1 - 1/2 + 1/2 - 1/3 + .. + 1/99 - 1/100 = 1 - 1/100 < 1 =>

C > 99 - 1 => C > 98