Question
limn→∞n∑r=1cot−1(r2+34) is
Answer: Option C
:
C
limn→∞n∑r=1tan−1(44r2+3)
=limn→∞n∑r=1tan−1(1r2−14+1)
=limn→∞n∑r=1tan−1((r+12)−(r−12)1+(r+12)(r−12))
=limn→∞n∑r=1tan−1{tan−1(r+12)−tan−1(r−12)}
=limn→∞{tan−1(n+12)−tan−1(12)}
= π2−tan−112
= tan−12
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:
C
limn→∞n∑r=1tan−1(44r2+3)
=limn→∞n∑r=1tan−1(1r2−14+1)
=limn→∞n∑r=1tan−1((r+12)−(r−12)1+(r+12)(r−12))
=limn→∞n∑r=1tan−1{tan−1(r+12)−tan−1(r−12)}
=limn→∞{tan−1(n+12)−tan−1(12)}
= π2−tan−112
= tan−12
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