n→∞limtan(r=1∑ntan−1(1+r(r+1)1))=n→∞limtan(r=1∑ntan−1(1+r(r+1)r+1−r))
=tan(n→∞limr=1∑n[tan−1(r+1)−tan−1(r)])
=tan(n→∞lim(tan−1(n+1)−4π))
=tan(4π)=1
n→∞limtanr=1∑ntan−1(1+r+r21) is equal to_______.
Held on 24 Feb 2021 · Verified 6 Jul 2026.
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