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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q. 14 (page 838)

In Problems 13鈥�16, find each sum.
${鈭�}_{k = 1}^{30} (k^{2} + 2)$

Short Answer

Expert verified

The sum is ${鈭�}_{k = 1}^{30} (k^{2} + 2) = 9515$

Step by step solution

01

Step 1. Given information.

The summation notation of the sequence is:

${鈭�}_{k = 1}^{30} (k^{2} + 2)$

02

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

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

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Most popular questions from this chapter

In Problems 51鈥�66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.

$1 - \frac{3}{4} + \frac{9}{16} - \frac{27}{64} + . . . .$

In Problems 71-82, find the sum of each sequence.

${鈭� k^{3}}_{k = 4}^{24}$

In Problems 17鈥�28, write down the first five terms of each sequence.

$\{t_{n}\} = \{\frac{{(- 1)}^{n}}{(n + 1 (n + 2)}\}$

In Problems 17鈥�28, write down the first five terms of each sequence.

$\{S_{n}\} = \{\frac{2^{n}}{3^{n} + 1}\}$

In Problems 37鈥�50, a sequence is defined recursively. Write down the first five terms.

$a_{1} = 1; a_{2} = 2; a_{n} = a_{n - 1} 路 a_{n - 2}$

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