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If $S_{n} = \frac{e^{1 / n}}{n^{2}} + \frac{2}{n^{2}} e^{2 / n} + \frac{3}{n^{2}} e^{3 / n} + \dots + \frac{1}{n} e$ then $lim_{n \to \infty} S_{n}$ is

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Sn=1n∑k=1n knek/nlimn→∞ Sn=∫01 xexdx=1.

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If Sn=e1/nn2+2n2e2/n+3n2e3/n+⋯+1ne then limn→∞ Sn is

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If $S_{n} = \frac{e^{1 / n}}{n^{2}} + \frac{2}{n^{2}} e^{2 / n} + \frac{3}{n^{2}} e^{3 / n} + \dots + \frac{1}{n} e$ then $lim_{n \to \infty} S_{n}$ is