Chapter 12: Q. 14 (page 838)

In Problems 13–16, find each sum.
$\sum_{k = 1}^{30} (k^{2} + 2)$

Short Answer

Expert verified

The sum is $\sum_{k = 1}^{30} (k^{2} + 2) = 9515$

Step by step solution

Step 1. Given information.

The summation notation of the sequence is:

$\sum_{k = 1}^{30} (k^{2} + 2)$

Step 2. Expand the summation by substituting values of k.

$\sum_{k = 1}^{30} (k^{2} + 2) = (1^{2} + 2) + (2^{2} + 2) + (3^{2} + 2) + . . . . . . . . . . . . . (30^{2} + 2) = (1^{2} + 2^{2} + 3^{2} + . . . . 30^{2}) + (2 + 2 + 2 . . . . . . . . . . 30 t i m e s) = 2 \times 30 + (1^{2} + 2^{2} + 3^{2} + . . . . 30^{2}) = 60 + \frac{30 (30 + 1) (2.30 + 1)}{6} = 60 + \frac{30 \times 31 (60 + 1)}{6} = 60 + 5 (61) (31)) = 60 + 9455 = 9515$

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In Problems 13–16, find each sum.
$\sum_{k = 1}^{30} (k^{2} + 2)$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Expand the summation by substituting values of k.

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In Problems 13–16, find each sum. ∑k=130k2+2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Expand the summation by substituting values of k.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Pure Maths

Mechanics Maths

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

In Problems 13–16, find each sum.
$\sum_{k = 1}^{30} (k^{2} + 2)$