Chapter 4: Q. 1 (page 404)

Calculating sums: Determine the value of each of the sums that
follow. Some can be computed directly, some require the use
of sum formulas, and for some you will have to also compute
a limit .
${\sum \frac{1}{k^{2}}}_{k = 1}^{10}$

Short Answer

Expert verified

The value is $\frac{1968329}{1270080}$ .

Step by step solution

Step 1. Given information .

Consider the given sigma function ${\sum \frac{1}{k^{2}}}_{k = 1}^{10}$ .

Step 2. Find the value .

Compute $a = 1, 2, 3 . . . . . . . . . . . . . . . 10$ in the given sigma function .

When k = 1 then role="math" localid="1648722671346" $\frac{1}{k^{2}} = \frac{1}{1^{^{2}}} = 1 = a_{1}$

k = 2 then $a_{2} = \frac{1}{4}$

k = 3 then $a_{3} = \frac{1}{9}$

k = 4 then $a_{4} = \frac{1}{16}$

k= 5 then $a_{5} = \frac{1}{25}$

k= 6 then $a_{6} = \frac{1}{36}$

k = 7 then $a_{7} = \frac{1}{49}$

k= 8 then $a_{8} = \frac{1}{64}$

k= 9 then $a_{9} = \frac{1}{81}$

k =10 then $a_{10} = \frac{1}{100}$

Compute the sum of $a_{k} = \frac{1}{k^{2}} = 1 . . . . . . . . . . . . . 10$ .

$= 1 + \frac{1}{4} + \frac{1}{9} + \frac{1}{16} + \frac{1}{25} + \frac{1}{36} + \frac{1}{49} + \frac{1}{64} + \frac{1}{81} + \frac{1}{100} = \frac{1968329}{1270080}$

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Calculating sums: Determine the value of each of the sums that
follow. Some can be computed directly, some require the use
of sum formulas, and for some you will have to also compute
a limit .
${\sum \frac{1}{k^{2}}}_{k = 1}^{10}$

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Find the value .

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Calculating sums: Determine the value of each of the sums thatfollow. Some can be computed directly, some require the useof sum formulas, and for some you will have to also computea limit .∑1k2k=110

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Find the value .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Decision Maths

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Study anywhere. Anytime. Across all devices.

Calculating sums: Determine the value of each of the sums that
follow. Some can be computed directly, some require the use
of sum formulas, and for some you will have to also compute
a limit .
${\sum \frac{1}{k^{2}}}_{k = 1}^{10}$