What is the limit as n approaches infinity of \sum_{k=1}^n(4+(3k)/n)^2(3/n) ?

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limit as n approaches infinity of \sum_{k=1}^n(4+(3k)/n)^2(3/n)

n \to \infty lim (k = 1 \sum n (4 + \frac{3 k}{n})^{2} (\frac{3}{n}))

93

Solution steps

n \to \infty lim (k = 1 \sum n (4 + \frac{3 k}{n})^{2} (\frac{3}{n}))

Apply the limit of sum formula:

\int_{0}^{3} (4 + x)^{2} d x

Solve

\int_{0}^{3} (4 + x)^{2} d x : 93

= 93

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What is the limit as n approaches infinity of \sum_{k=1}^n(4+(3k)/n)^2(3/n) ?
The limit as n approaches infinity of \sum_{k=1}^n(4+(3k)/n)^2(3/n) is 93