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The value of sum(n=1)^1000 int(n-1)^n e^...

The value of `sum_(n=1)^1000 int_(n-1)^n e^(x-[x])dx`, where `[x]` is the greatest integer function, is (A) `(e^1000-1)/1000` (B) `(e-1)/1000` (C) `(e^1000-1)/(e-1)` (D) `1000(e-1)`

A

`(e^(1000)-1)/( 1000)`

B

`(e^(1000)-1)/( e-1)`

C

`1000 (e-1)`

D

`(e-1)/( 1000)`

Text Solution

Verified by Experts

The correct Answer is:
C
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