Q. 13 Write the sum 2+24+29+216+225in ... [FREE SOLUTION]

Chapter 4: Q. 13 (page 325)

Write the sum $2 + \frac{2}{4} + \frac{2}{9} + \frac{2}{16} + \frac{2}{25}$ in sigma notation in three ways: with a starting value of $(a) k = 1, (b) k = 2, (c) k = 0$

Short Answer

Expert verified

$Part (a) {鈭�}_{k = 1}^{5} \frac{2}{k^{2}} Part (b) {鈭�}_{k = 2}^{6} \frac{2}{{(k - 1)}^{2}} Part (c) {鈭�}_{k = 0}^{4} \frac{2}{{(k + 1)}^{2}}$

Step by step solution

Part(a) Step 1. Given Information

The given sum is $2 + \frac{2}{4} + \frac{2}{9} + \frac{2}{16} + \frac{2}{25}$

Part(a) Step 2. Calculation

The sum can be written as follows,

$2 + \frac{2}{4} + \frac{2}{9} + \frac{2}{16} + \frac{2}{25} = \frac{2}{1^{2}} + \frac{2}{2^{2}} + \frac{2}{3^{2}} + \frac{2}{4^{2}} + \frac{2}{5^{2}} = {鈭�}_{k = 1}^{5} \frac{2}{k^{2}}$

Part(b) Step 1. Calculation

The sum can be written as follows,

$2 + \frac{2}{4} + \frac{2}{9} + \frac{2}{16} + \frac{2}{25} = \frac{2}{{(2 - 1)}^{2}} + \frac{2}{{(3 - 1)}^{2}} + \frac{2}{{(4 - 1)}^{2}} + \frac{2}{{(5 - 1)}^{2}} + \frac{2}{{(6 - 1)}^{2}} = {鈭�}_{k = 2}^{6} \frac{2}{{(k - 1)}^{2}}$

Part(c) Step 1. Calculation

The sum can be written as follows,

$2 + \frac{2}{4} + \frac{2}{9} + \frac{2}{16} + \frac{2}{25} = \frac{2}{{(0 + 1)}^{2}} + \frac{2}{{(1 + 1)}^{2}} + \frac{2}{{(2 + 1)}^{2}} + \frac{2}{{(3 + 1)}^{2}} + \frac{2}{{(4 + 1)}^{2}} = {鈭�}_{k = 0}^{4} \frac{2}{{(k + 1)}^{2}}$

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Write the sum $2 + \frac{2}{4} + \frac{2}{9} + \frac{2}{16} + \frac{2}{25}$ in sigma notation in three ways: with a starting value of $(a) k = 1, (b) k = 2, (c) k = 0$

Short Answer

Step by step solution

Part(a) Step 1. Given Information

Part(a) Step 2. Calculation

Part(b) Step 1. Calculation

Part(c) Step 1. Calculation

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91影视

Write the sum 2+24+29+216+225in sigma notation in three ways: with a starting value of(a)k=1,(b)k=2,(c)k=0

Short Answer

Step by step solution

Part(a) Step 1. Given Information

Part(a) Step 2. Calculation

Part(b) Step 1. Calculation

Part(c) Step 1. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Statistics

Mechanics Maths

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Write the sum $2 + \frac{2}{4} + \frac{2}{9} + \frac{2}{16} + \frac{2}{25}$ in sigma notation in three ways: with a starting value of $(a) k = 1, (b) k = 2, (c) k = 0$