MathDB

6

Part of 2019 ISI Entrance Examination

Problems(1)

ISI 2019 : Problem #6

Source: I.S.I. 2019

5/5/2019
For all natural numbers nn, let A_n=\sqrt{2-\sqrt{2+\sqrt{2+\cdots+\sqrt{2}}}} \text{(n many radicals)} (a) Show that for n⩾2n\geqslant 2, An=2sin⁡π2n+1A_n=2\sin\frac{\pi}{2^{n+1}} (b) Hence or otherwise, evaluate the limit lim⁡n→∞2nAn\lim_{n\to\infty} 2^nA_n
isiIndian Statistical InstitutelimitSequencereal analysis