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Please solve the problem in the attachment ......... ANS is 1..........
Write pi√(n^2+n) as npi√(1+1/n)Now using binomial theorem for fractional indices, expand (1+1/n)^1/2 as 1+1/2n+O(1/n^2)Multiply by npi and take cosinecos(npi+pi/2+O(1/n)) = - sin(npi+O(1/n))As n tends to infinity, O(1/n) becomes zero.Also, sinnpi is always zero as long as n is an integer. So the limit is zero. so your answer 1 is clearly wrong so kindly recheck and revert back if you have any doubts.
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