Q. 15 Sums and Constant Multiples of C... [FREE SOLUTION]

Chapter 7: Q. 15 (page 655)

Sums and Constant Multiples of Convergent Series:
If ${鈭�}_{k = 1}^{鈭�} a_{k} a n d {鈭�}_{k = 1}^{鈭�} b_{k}$ are convergent series and c is any real number, then
${鈭�}_{k = 1}^{鈭�} (a_{k} + b_{k}) =+_$

Short Answer

Expert verified

The required answer is ${鈭�}_{k = 1}^{鈭�} (a_{k} + b_{k}) = {鈭�}_{k = 1}^{鈭�} (a_{k}) + {鈭�}_{k = 1}^{鈭�} (b_{k})$

Step by step solution

Step 1. Given Information

The given data is If ${鈭�}_{k = 1}^{鈭�} a_{k} a n d {鈭�}_{k = 1}^{鈭�} b_{k}$ are convergent series andc is any real number.

Step 2. Explanation

As we know that sum of two convergent series can be written as

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

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Sums and Constant Multiples of Convergent Series:
If ${鈭�}_{k = 1}^{鈭�} a_{k} a n d {鈭�}_{k = 1}^{鈭�} b_{k}$ are convergent series and c is any real number, then
${鈭�}_{k = 1}^{鈭�} (a_{k} + b_{k}) =+_$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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Sums and Constant Multiples of Convergent Series:If 鈭�k=1鈭�akand鈭�k=1鈭�bkare convergent series and c is any real number, then鈭�k=1鈭�(ak+bk)=____+_____

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Statistics

Discrete Mathematics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Sums and Constant Multiples of Convergent Series:
If ${鈭�}_{k = 1}^{鈭�} a_{k} a n d {鈭�}_{k = 1}^{鈭�} b_{k}$ are convergent series and c is any real number, then
${鈭�}_{k = 1}^{鈭�} (a_{k} + b_{k}) =+_$