The sum of the first 20 terms of the series `(1)/(5xx6)` +` (1)/(6xx7)` + `(1)/(7xx8 )` + ..... is: Options: A . &nbsp0.16 B . &nbsp1.6 C . &nbsp16 D . &nbspNone of these

The sum of the f

Question

The sum of the first 20 terms of the series `(1)/(5xx6)` +` (1)/(6xx7)` + `(1)/(7xx8 )` + ..... is:

Options:

A . 0.16

B . 1.6

C . 16

D . None of these

Answer: Option A

Given expression = `(1)/(5xx6)` + `(1)/(6xx7)` +`(1)/(7xx8)` +..........+ `(1)/(24xx25)`

= `(1/5 -1/6)` +`(1/6 - 1/7)` + `(1/7 - 1/8)` +...........+ `(1/24 - 1/25)`

= `(1/5 - 1/25)` = `4/25`= 0.16.

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