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Q.

If ∑r=1∞ tan−1⁡12r2=t,  then tan t is equal to

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a

0

b

1

c

3

d

1/3.

answer is B.

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Detailed Solution

∑r=1∞ tan−1⁡12r2=∑1∞ tan−1⁡(2r+1)−tan−1⁡(2r−1)=tan−1⁡3−tan−1⁡1+tan−1⁡5−tan−1⁡3+…=π/2−π/4=π/4
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