Chapter 12: Q. 256 (page 1217)

In the following exercises, expand the partial sum and find its value.
$\sum_{k = 1}^{4} (k + 1) (2 k + 1)$

Short Answer

Expert verified

The partial sum is $94$ .

Step by step solution

Step 1. Given information.

The given expression is,

$\sum_{k = 1}^{4} (k + 1) (2 k + 1)$ .

Step 2. Finding the partial sum.

Now, to expand the partial sum we will substitute $1, 2, 3,$ and $4$ respectively and then simplify.

$\sum_{k = 1}^{4} (k + 1) (2 k + 1) = (1 + 1) (2 (1) + 1) + (2 + 1) (2 (2) + 1) + (3 + 1) (2 (3) + 1) + (4 + 1) (2 (4) + 1) = (2) (3) + (3) (5) + (4) (7) + (5) (9) = 6 + 15 + 28 + 45 = 94$

Therefore, the partial sum is $94$ .

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In the following exercises, expand the partial sum and find its value.
$\sum_{k = 1}^{4} (k + 1) (2 k + 1)$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding the partial sum.

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In the following exercises, expand the partial sum and find its value.
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