can i get step by step help please k=1k=1Evaluate the sums in Exercises 19–36. k327.2 225k=1k=1

Name: can i get step by step help please k=1k=1Evaluate the sums in Exercise
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Description: can i get step by step help please k=1k=1Evaluate the sums in Exercises 19–36. k327.2 225k=1k=1

Answered: k=1 k=1 Evaluate the sums in Exercises…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 49E

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can i get step by step help please

k=1
k=1
Evaluate the sums in Exercises 19–36.

Expert Solution

Step 1

There are two terms in the series above. We will evaluate them one by one and then add them up to get the final answer.

Step 2

First term

$\sum_{k=1}^{5}\frac{k^3}{225}=\frac{1}{225}\sum_{k=1}^{5}k^3$

Recall the formula for the sum of the cubes of the first n natural numbers.

Step 3

Hence, the first term becomes:

$\sum_{k=1}^{5}\frac{k^3}{225}=\frac{1}{225}\sum_{k=1}^{5}k^3=\frac{1}{225}\times [\frac{(5(5+1))}{2}]^2==\frac{1}{225}\times15^2=\frac{1}{225}\times225=1$

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