Question

[TXT Channel Funfun]

So sánh A = \(\dfrac{1}{1.2^2}+\dfrac{1}{2.3^2}+...+\dfrac{1}{49.50^2}\)với \(\dfrac{1}{2}\)

Answer 1

[Đào Thị Phượng]

Ta có A = 1 / 2 . ( 1 - 1 / 2 + 1 / 2 - 1/ 3 + ............+ 1 / 49 - 1 / 50 )

= 1/ 2 . 1 + ( -1/2 + 1/2 ) + ...........+ ( - 1/49 + 1/49 ) -1/50

=1/2 + 0 + 0 + .................+ 0 - 1/50

= 1/2 - 1/50

=12/25

Vậy A = 12/25

Ta có 12/25 < 1/2

vậy 25/12 < 1/2