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Question

If y=tan111+x+x2+tan11x2+3x+3+tan11x2+5x+7++ upto n terms, then y(0) is equal to

A
11+n2
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B
n21+n2
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C
n1+n2
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D
None of these
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Solution

The correct option is B n21+n2
y=tan111+x+x2+tan11x2+3x+3++n terms
=tan1(x+1)x1+x(1+x)+tan1(x+2)(x+1)1+(x+1)(x+2)++n terms
=tan1(x+1)tan1x+tan1(x+2)tan1(x+1)++tan1(x+n)tan1(x+(n1))
=tan1(x+n)tan1x
y(x)=11+(x+n)211+x2
y(0)=11+n21=n21+n2

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