Question

Express the following sum in closed form. sum_{k=1}^{n} left(4 + 3 cdot frac{k}{n} ight)^{2} = Hint: Start by multiplying out left(4 + 3 cdot frac{k}{n} ight)^{2}. Note: Your answer should be in terms of n.

          Express the following sum in closed form.
sum_{k=1}^{n} left(4 + 3 cdot frac{k}{n}
ight)^{2} =
Hint: Start by multiplying out left(4 + 3 cdot frac{k}{n}
ight)^{2}.
Note: Your answer should be in terms of n.

$Express the following sum in closed form. sumk=1^n left(4 + 3 cdot frackn ight)^2 = Hint: Start by multiplying out left(4 + 3 cdot frackn ight)^2. Note: Your answer should be in terms of n.$

Added by Steven E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zhumagali Shomanov

08/14/2023

Step 1

Let's denote this sum as $S_n$: $S_n = \sum_{k=1}^n (4 + 3k^2 - 3k)$ We can split this sum into three separate sums: $S_n = \sum_{k=1}^n 4 + \sum_{k=1}^n 3k^2 - \sum_{k=1}^n 3k$ Now, we can use the formulas for the sum of the first $n$ integers, the sum of the Show more…

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