8Let s, be the n-th partial sum; that is,Consider the seriesn+ 10n=18Sn%Di+ 10i=1Find s4 and SgS4 =Sg =

The n the partial sum of series is given by sn=∑i=1n8i+10. Evaluate s4 as follows.…

Answered: 8. Let s, be the n-th partial sum; that…

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8. Let s, be the n-th partial sum; that is, Consider the series n+ 10 n=1 8 Sn i+ 10 and s8

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.4: Series And Their Notations

Problem 1SE: What is an nth partial sum?

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Question

8
Let s, be the n-th partial sum; that is,
Consider the series
n+ 10
n=1
8
Sn
%D
i+ 10
i=1
Find s4 and Sg
S4 =
Sg =

Expert Solution

Step 1

The n the partial sum of series is given by $s_{n} = \sum_{i = 1}^{n} \frac{8}{i + 10}$ .

Evaluate s₄ as follows.

$\begin{array}{rcl} s_{4} & = & \sum_{i = 1}^{4} \frac{8}{i + 10} \\ = & \frac{8}{1 + 10} + \frac{8}{2 + 10} + \frac{8}{3 + 10} + \frac{8}{4 + 10} \\ = & \frac{8}{11} + \frac{8}{12} + \frac{8}{13} + \frac{8}{14} \\ = & 8 (\frac{1}{11} + \frac{1}{12} + \frac{1}{13} + \frac{1}{14}) \\ = & 8 (0.32259) \\ = & 2.58072 \\ \approx & 2.581 \end{array}$

Therefore, the value of the partial sum s₄ is 2.581.

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