Question

Tính :

A= -1 - 1/3 - 1/6 - 1/10 - 1/15 - ...  1/1225 

Answer 1

\(A=-1-\dfrac{1}{3}-...-\dfrac{1}{1225}\)

\(=-\dfrac{2}{2}-\dfrac{2}{6}-...-\dfrac{2}{2450}\)

\(=-2\left(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{2450}\right)\)

\(=-2\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)\)

\(=-2\left(1-\dfrac{1}{50}\right)=-2\cdot\dfrac{49}{50}=-\dfrac{49}{25}\)

Answer 2

`A = -1 - 1/3 - 1/6 - 1/10 - 1/15 - ... - 1/1225`

`A = -2/2 - 2/6 - 2/12 - ... - 1/2450`

`A = -2 . (1/2 + 1/6 + ... + 1/2450)`

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

`A = -2 . (1-1/50)`

`A = -2 . 49/50`

`A = -49/25`