What is the limit as n approaches infinity of \sum_{i=1}^n(i^3)/(n^4)+1/n ?

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limit as n approaches infinity of \sum_{i=1}^n(i^3)/(n^4)+1/n

n \to \infty lim (i = 1 \sum n \frac{i ^{3}}{n ^{4}} + \frac{1}{n})

\frac{5}{4}

Decimal

1.25

Solution steps

n \to \infty lim (i = 1 \sum n \frac{i ^{3}}{n ^{4}} + \frac{1}{n})

Apply the limit of sum formula:

\int_{0}^{1} x^{3} + 1 d x

Solve

\int_{0}^{1} x^{3} + 1 d x : \frac{5}{4}

= \frac{5}{4}

What is the limit as n approaches infinity of \sum_{i=1}^n(i^3)/(n^4)+1/n ?
The limit as n approaches infinity of \sum_{i=1}^n(i^3)/(n^4)+1/n is 5/4