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The value of 1/(2!) +2/(3!) +...+999/(1...

The value of `1/(2!) +2/(3!) +...+999/(1000!)` is equal to

A

`(1000!-1)/(1000!)`

B

` (1000!+1)/(1000!)`

C

`(999!-1)/(999)`

D

`(999!+1)/(999)`

Text Solution

Verified by Experts

The correct Answer is:
a
` 1/(2!) +2/(3!) + 999/(1000!) = (2-1)/(3!) +(3-1)/(3!) +...+ (1000-1)/(1000!)`
` = 1/(1!) -1/(2!) +1/(2!) -1/(3!)+1/(999!)-1/(1000!)`
` 1- 1/(1000!) = (1000!-1)/(1000!)`
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  1. The value of 1/(2!) +2/(3!) +...+999/(1000!) is equal to

    Text Solution

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