Calculus Examples

$\sum_{n = 1}^{5} 2 n + (n^{2} + 1)$

Step 1

Simplify the summation.

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Step 1.1

Remove unnecessary parentheses.

$2 n + n^{2} + 1$

Step 1.2

Rewrite the summation.

$\sum_{n = 1}^{5} 2 n + n^{2} + 1$

Step 2

Expand the series for each value of $n$ .

$2 \cdot 1 + 1^{2} + 1 + 2 \cdot 2 + 2^{2} + 1 + 2 \cdot 3 + 3^{2} + 1 + \dots + 2 \cdot 5 + 5^{2} + 1$

Step 3

Simplify the expanded form.

$90$