HPCET Power Sum Limit — practice questions

Explore 1 free Power Sum Limit questions in HPCET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Power Sum Limit questions and exercises with answers

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Evaluate $\displaystyle\lim_{n\to\infty} \dfrac{1^k + 2^k + \cdots + n^k}{n^{k+1}}$ for $k > -1$:Read the answer and worked solution →

Worked practice questions

Evaluate $\displaystyle\lim_{n\to\infty} \dfrac{1^k + 2^k + \cdots + n^k}{n^{k+1}}$ for $k > -1$:

$0$
$\dfrac{1}{k+1}$
$1$
$k$

Show answer and solution

Correct answer: B. $\dfrac{1}{k+1}$

Recognise as Riemann sum: $\sum (r/n)^k \cdot (1/n) \to \int_0^1 x^k\, dx = 1/(k+1)$.

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HPCET Power Sum Limit — practice questions

Power Sum Limit questions and exercises with answers

Worked practice questions

Evaluate $\displaystyle\lim_{n\to\infty} \dfrac{1^k + 2^k + \cdots + n^k}{n^{k+1}}$ for $k > -1$:

How to practise

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