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("lim")(xvecoo)sum(x=1)^(20)cos^(2n)(x-1...

`("lim")_(xvecoo)sum_(x=1)^(20)cos^(2n)(x-10)i se q u a lto` 0 (b) 1 (c) 19 (d) 20

A

(a) 2

B

(b) -2

C

(c) 1

D

(d) -1

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(ntooo)limcos^(2n)x={{:(1", "x=rpi","r inl),(0", "xnerpi","r inl):}`
Here, for `x=10`, `underset(ntooo)limcos^(2n)(x-10)=1` and in all other cases, it is zero. Therefore,
`underset(ntooo)limsum_(x=1)^(oo)cos^(2n)(x-10)=1`
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