Chapter 12: Q 81. (page 809)

In Problems 71-82, find the sum of each sequence.
${\sum k^{3}}_{k = 5}^{20}$

Short Answer

Expert verified

The sum of this sequence is 44000.

Step by step solution

Step 1. Write the given information.

The sum of sequence:

${\sum k^{3}}_{k = 5}^{20}$

Step 2. Use the properties of sequence.

Using the properties of sequence:

${\sum k^{3}}_{k = j + 1}^{n} = {\sum k^{3}}_{k = 1}^{n} {- \sum k^{3}}_{k = 1}^{j} S o, {\sum k^{3}}_{k = 5}^{20} = {\sum k^{3}}_{k = 1}^{20} {- \sum k^{3}}_{k = 1}^{4}$

Step 3. Use the formula for sum of sequences of (n3 ), n - real numbers.

The formula for summation:

${\sum k^{3}}_{k = 1}^{n} = 1^{3} + 2^{3} + . . . + n^{3} \Rightarrow {\sum k^{3}}_{k = 1}^{n} = {[\frac{n (n + 1)}{2}]}^{2}$

So,

${\sum k^{3}}_{k = 5}^{20} = {\sum k^{3}}_{k = 1}^{20} {- \sum k^{3}}_{k = 1}^{4} \Rightarrow {\sum k^{3}}_{k = 5}^{20} = {[\frac{20 (20 + 1)}{2}]}^{2} - {[\frac{4 (4 + 1)}{2}]}^{2} \Rightarrow {\sum k^{3}}_{k = 5}^{20} = {[10 \times 21]}^{2} - {[2 \times 5]}^{2} \Rightarrow {\sum k^{3}}_{k = 5}^{20} = 44100 - 100 \Rightarrow {\sum k^{3}}_{k = 5}^{20} = 44000$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 71-82, find the sum of each sequence.
${\sum k^{3}}_{k = 5}^{20}$

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 (n3 ), n - real numbers.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Pure Maths

Discrete Mathematics

Mechanics Maths

Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems 71-82, find the sum of each sequence.∑k3k=520

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 (n3 ), n - real numbers.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Pure Maths

Discrete Mathematics

Mechanics Maths

Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems 71-82, find the sum of each sequence.
${\sum k^{3}}_{k = 5}^{20}$