a. Find an upper bound for the remainder in terms of n.

b. Find how many terms are needed to ensure that the remainder is less than

c. Find lower and upper bounds (ln and Un, respectively) on the exact value of the series.

slaggingV
2021-02-06
Answered

Consider the following convergent series.

a. Find an upper bound for the remainder in terms of n.

b. Find how many terms are needed to ensure that the remainder is less than${10}^{-3}$ .

c. Find lower and upper bounds (ln and Un, respectively) on the exact value of the series.

$\sum _{k=1}^{\mathrm{\infty}}\frac{1}{{3}^{k}}$

a. Find an upper bound for the remainder in terms of n.

b. Find how many terms are needed to ensure that the remainder is less than

c. Find lower and upper bounds (ln and Un, respectively) on the exact value of the series.

You can still ask an expert for help

Neelam Wainwright

Answered 2021-02-07
Author has **102** answers

Given,

We are answering the first three subparts as per our honor code.

The series

Calculation

(a). Find an upper bound for the remainder in terms of n.

Since we know that

Hence an upper bound for the remainder in terms of n is

(b) Find how many terms are needed to ensure that the remainder is less than

Since given

(c). Find lower and upper bounds (

Since

Jeffrey Jordon

Answered 2021-12-16
Author has **2262** answers

Answer is given below (on video)

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