Q 78. In Problems 71-82, find the sum ... [FREE SOLUTION]

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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 78. (page 809)

In Problems 71-82, find the sum of each sequence.
${鈭� (k^{2}}_{k = 0}^{14} - 4)$

Short Answer

Expert verified

The sum of this sequence is 955.

Step by step solution

Step 1. Write the given information.

The sum of sequence:

${鈭� (k^{2} - 4)}_{k = 0}^{14}$

Step 2. Use the properties of sequence.

Using the properties of sequence:

${鈭� (a_{k} - b_{k})}_{k = 1}^{n} = {鈭� (a_{k})}_{k = 1}^{n} {- 鈭� (b_{k})}_{k = 1}^{n}$

So,

${鈭� (k^{2} - 4)}_{k = 1}^{14} = {鈭� (k^{2})}_{k = 1}^{14} {- 鈭� (4)}_{k = 1}^{14}$

Step 3. Use the formula for sum of sequences of (n2 ), n - real numbers.

Using formula for summation is:

${鈭� k^{2}}_{k = 0}^{n} = 1^{2} + 2^{2} + . . . + n^{2} {鈭� k^{2}}_{k = 0}^{n} = 0 + {鈭� k^{2}}_{k = 1}^{n} 鈬� {鈭� k^{2}}_{k = 0}^{n} = 0 + \frac{n (n + 1) (2 n + 1)}{6}$

So,

${鈭� k^{2}}_{k = 0}^{14} = \frac{14 (14 + 1) ((2 脳 14) + 1)}{6} 鈬� {鈭� k^{2}}_{k = 0}^{14} = \frac{6090}{6} 鈬� {鈭� k^{2}}_{k = 0}^{14} = 1015$

Step 4. Use the formula for sum of sequences.

Using formula for summation is:

${鈭� c}_{k = 0}^{n} = c + c + . . . + c 鈬� {鈭� c}_{k = 0}^{n} = c n, c - r e a l n u m b e r S o, {鈭� 4}_{k = 0}^{14} = 4 脳 (14 + 1) 鈬� {鈭� 4}_{k = 0}^{14} = 4 脳 15 鈬� {鈭� 4}_{k = 0}^{14} = 60$

Step 5. Now, subtract Step 3 from Step 4.

From Step 3,

${鈭� k^{2}}_{k = 1}^{14} = 1015$

From Step 4,

${鈭� 4}_{k = 1}^{14} = 60$

So,

${鈭� (k^{2} - 4)}_{k = 1}^{14} = {鈭� (k^{2})}_{k = 1}^{14} {- 鈭� (4)}_{k = 1}^{14} 鈬� {鈭� (k^{2} - 4)}_{k = 1}^{14} = 1015 - 60 鈬� {鈭� (k^{2} - 4)}_{k = 1}^{14} = 955$

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91影视

In Problems 71-82, find the sum of each sequence.
${鈭� (k^{2}}_{k = 0}^{14} - 4)$

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Use the properties of sequence.

Step 3. Use the formula for sum of sequences of (n2 ), n - real numbers.

Step 4. Use the formula for sum of sequences.

Step 5. Now, subtract Step 3 from Step 4.

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91影视

In Problems 71-82, find the sum of each sequence.鈭�(k2k=014-4)

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Use the properties of sequence.

Step 3. Use the formula for sum of sequences of (n2 ), n - real numbers.

Step 4. Use the formula for sum of sequences.

Step 5. Now, subtract Step 3 from Step 4.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

In Problems 71-82, find the sum of each sequence.
${鈭� (k^{2}}_{k = 0}^{14} - 4)$