lim n → ∞ 1 1 + n + 1 2 + n + 1 3 + n + … + 1 2 n is equal to :-

Question

lim n &#8594; &#8734; 1 1 + n + 1 2 + n + 1 3 + n + &#8230; + 1 2 n is equal to :-

Aicharya · Accepted Answer

We have, lim n &#8594; &#8734; 1 1 + n + 1 2 + n + 1 3 + n + &#8230; + 1 2 n = lim n &#8594; &#8734; 1 1 + n + 2 1 + n + 3 1 + n + &#8230; . + 1 n + n = lim n &#8594; &#8734; &#8721; &#160; r = 1 n 1 n + r = lim n &#8594; &#8734; &#160; &#8721; r = 1 n 1 n 1 1 + r n = &#8747; 0 1 1 1 + x d x = log e 1 + x 0 1 = log e 2

lim n &#8594; &#8734; 1 1 + n + 1 2 + n + 1 3 + n + &#8230; + 1 2 n is equal to :-

Solution

lim n → ∞ 1 1 + n + 1 2 + n + 1 3 + n + … + 1 2 n is equal to :-