If a - limn-tan -22 - -23 - - - -2n - 1 2n - 1- then value of - a is

Given: a=lim _ n→∞ #160; tan( π #160; 2 ^ 2 +π #160; 2 ^ 3 +.....π #160; 2 ^ n+1 #160; ) #160; 2 ^ n 1 #160; To find: Value of ...

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Substitution Method to Remove Indeterminate Form

If a = limn...

Question

If $a = lim n \to \infty \frac{tan (\frac{π}{2^{2}} + \frac{π}{2^{3}} + . . . . + \frac{π}{2^{n + 1}})}{2^{n - 1}}$ , then value of $π a$ is

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lim n \to \infty \frac{π}{6 n} [{sec}^{2} (\frac{π}{6 n}) + {sec}^{2} (2 \cdot \frac{π}{6 n}) + \dots + {sec}^{2} ((n - 1) \frac{π}{6 n}) + \frac{4}{3}]

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