Let I(n)=underset(0)overset(pi//2)intx^(...

Let `I_(n)=underset(0)overset(pi//2)intx^(n)cosxdx,` where in is a non-negative integer
Then `underset(n=2)overset(oo)sum((I_(n))/(n!)+(I_(n-2))/((n-2)!))` equals-

A

`e^(pi//2) - 1 - pi/2`

B

`e^(pi//2)-1`

C

`e^(pi//2) - pi/2`

D

`e^(pi//2)`

Verified by Experts

The correct Answer is:

A

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