Q. 14 Split the sum 鈭慿=411聽k聽into ... [FREE SOLUTION]

Chapter 4: Q. 14 (page 325)

Split the sum ${鈭�}_{k = 4}^{11} \sqrt{k}$ into three sums, each in sigma notation, where the first sum has two terms and the last two sums each have three terms.

Short Answer

Expert verified

The solution is: ${鈭�}_{k - 4}^{11} \sqrt{k} = {鈭�}_{k - 4}^{5} \sqrt{k} + {鈭�}_{k - 6}^{8} \sqrt{k} + {鈭�}_{k - 9}^{11} \sqrt{k}$

Step by step solution

Step 1. Given Information.

Consider the given question,

${鈭�}_{k = 4}^{11} \sqrt{k}$

Step 2. Calculation

Consider the given sum-

${鈭�}_{k - 4}^{11} \sqrt{k}$

Here k varies from $4 t o 11$

So, it can be divided into three sums as shown:

${鈭�}_{k - 4}^{11} \sqrt{k} = {鈭�}_{k - 4}^{5} \sqrt{k} + {鈭�}_{k - 6}^{8} \sqrt{k} + {鈭�}_{k - 9}^{11} \sqrt{k}$

Now, ${鈭�}_{k - 4}^{5}$ has two terms in the sums as $\sqrt{4} + \sqrt{5}$

${鈭�}_{k - 6}^{8} \sqrt{k}$ has three terms in the sum as $\sqrt{6} + \sqrt{7} + \sqrt{8}$

${鈭�}_{k - 9}^{11} \sqrt{k}$ has three terms in the sum as $\sqrt{9} + \sqrt{10} + \sqrt{11} .$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Split the sum ${鈭�}_{k = 4}^{11} \sqrt{k}$ into three sums, each in sigma notation, where the first sum has two terms and the last two sums each have three terms.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Pure Maths

Decision Maths

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

91影视

Split the sum 鈭�k=411kinto three sums, each in sigma notation, where the first sum has two terms and the last two sums each have three terms.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Pure Maths

Decision Maths

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Split the sum ${鈭�}_{k = 4}^{11} \sqrt{k}$ into three sums, each in sigma notation, where the first sum has two terms and the last two sums each have three terms.