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Question

If y=tan111+x+x2+tan11x2+3x+3
+tan11x2+5x+7++ upto n terms, then

A
y(0)=n21+n2
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B
y(0)=n21+n2
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C
y(n)=n21+n2
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D
y(n)=n21+n2
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Solution

The correct option is C y(n)=n21+n2
y=tan111+x+x2+tan11x2+3x+3++ upto n terms
=tan1(x+1)x1+x(1+x)+tan1(x+2)(x+1)1+(x+1)(x+2)++ upto 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
y(n)=111+n2=n21+n2

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