Asked by sidra jawad on Jul 09, 2024

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Find the sum. ∑n=0∞(−38) n\sum_{n=0}^{\infty}\left(-\frac{3}{8}\right) ^{n}n=0(83) n

A) 811\frac{8}{11}118
B) 314\frac{3}{14}143
C) 58\frac{5}{8}85
D) 85\frac{8}{5}58
E) 35\frac{3}{5}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.
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CJ
carissa juarez

1 week ago

Final Answer :
A
Explanation :
This is a geometric series with the first term a=1a = 1a=1 (since (−3/8)0=1(-3/8)^0 = 1(3/8)0=1 ) and common ratio r=−3/8r = -3/8r=3/8 . The sum of an infinite geometric series is given by S=a1−rS = \frac{a}{1 - r}S=1ra , provided ∣r∣<1|r| < 1r<1 . Substituting a=1a = 1a=1 and r=−3/8r = -3/8r=3/8 , we get S=11−(−3/8)=11+3/8=111/8=811S = \frac{1}{1 - (-3/8)} = \frac{1}{1 + 3/8} = \frac{1}{11/8} = \frac{8}{11}S=1(3/8)1=1+3/81=11/81=118 .