Limit problem: lim [n -> infty] [(1 + 2^p + 3^p + ... + n^p)/(n^{p+1})]

emmablom said:

I was wondering which areas this math problem involves in? I'm currently reading a course in calculus and I do not recognize the problem in my course literature .
Would be grateful if you could list the parts that you need to solve this problem.

. . .\(\displaystyle \mbox{For }\, p\, >\, 0,\, \mbox{ solve the following:}\)

. . . . .\(\displaystyle \displaystyle \lim_{n \rightarrow \infty}\, \dfrac{1\, +\, 2^p\, +\, 3^p\, +\, ...\, +\, n^p}{n^{p+1}}\)

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emmablom said:

The question is from a previous test in the course and I wonder what part chapter I can read in order to fully understand the problem?

. . .\(\displaystyle \mbox{For }\, p\, >\, 0,\, \mbox{ solve the following:}\)

. . . . .\(\displaystyle \displaystyle \lim_{n \rightarrow \infty}\, \dfrac{1\, +\, 2^p\, +\, 3^p\, +\, ...\, +\, n^p}{n^{p+1}}\)

This is what my course literature covers.

Iterations

Newton-Raphson's Method

Series: convergence / divergence, integral criterion
. . . . ..comparison criteria
. . . . ..root / quota criteria
. . . . ..Alternating series
. . . . ..Leibniz criterion
. . . . ..rearrangement of series
. . . . ..Power series
. . . . ..Taylor series
. . . . ..Power series convergence
. . . . ..Derivation / integration of power series

solution of differential equations

Sequences, series of functions

pointwise and uniform convergence

Dominated convergence

reversal of border processes

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