Asked by sidra jawad on Jul 09, 2024

Verified

Find the sum. $∑_{n=0}(−83 )_{n}$

A) $118 $

B) $143 $

C) $85 $

D) $58 $

E) $53 $

A) $118 $

B) $143 $

C) $85 $

D) $58 $

E) $53 $

Infinite Series

A sum of infinitely many terms following a specific pattern.

Sum

The outcome of summing two or more numbers.

- Gain an understanding of geometric series and employ this concept in the resolution of practical issues, inclusive of infinite series.

Verified Answer

CJ

carissa juarez

1 week ago

Final Answer :

A

Explanation :

This is a geometric series with the first term $a=1$ (since $(−3/8)_{0}=1$ ) and common ratio $r=−3/8$ . The sum of an infinite geometric series is given by $S=1−ra $ , provided $∣r∣<1$ . Substituting $a=1$ and $r=−3/8$ , we get $S=1−(−3/8)1 =1+3/81 =11/81 =118 $ .

## Learning Objectives

- Gain an understanding of geometric series and employ this concept in the resolution of practical issues, inclusive of infinite series.

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