\lim_{\n\to\infty} {1^2+2^2+....+\n^2}/\n^3

TS ICET 24 May 2018 Shift 1 Paper

Question : 134 of 200

Marks: +1, -0

\lim↙{\n→∞} {1^2+2^2+....+\n^2}/\n^3

Solution:

\text "Lt"↙{n → ∞}\;{1^{2}+2^{2}+⋅s+n^{2}}/{n^{3}}

\text "Lt"↙{n → ∞} \;{n(n+1)(2 n+1)}/{6 n^{3}}

\text "Lt"↙{n → ∞} \;{(1+{1}/{n})(2+{1}/{n})}/{6}

Where

n → ∞ \;{1}/{ n } → 0

=\;{(1)(2)}/{6}=\;{1}/{3}

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