Find the sum. \sum_{n=0}^{\infty}\left(-\frac{3}{8}\right)^{n} A) \frac{8}{11} B) \frac{3}{14} C) \frac{5}{8} D) \frac{8}{5} E) \frac{3}{5}

Question

Find the sum.  \sum_{n=0}^{\infty}\left(-\frac{3}{8}\right)^{n}  A)  \frac{8}{11}  B)  \frac{3}{14}  C)  \frac{5}{8}  D)  \frac{8}{5}  E)  \frac{3}{5}

carissa juarez · Accepted Answer

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 = \frac{a}{1 - r} , provided  |r| < 1 . Substituting  a = 1  and  r = -3/8 , we get  S = \frac{1}{1 - (-3/8)} = \frac{1}{1 + 3/8} = \frac{1}{11/8} = \frac{8}{11} .

Find the sum. $n\sum_{n=0}^{\infty}\left(-\frac{3}{8}\right) ^{n}$

A) $811\frac{8}{11}$
B) $314\frac{3}{14}$
C) $58\frac{5}{8}$
D) $85\frac{8}{5}$
E) $35\frac{3}{5}$

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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​

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Learning Objectives

Learning Objectives

Related questions

Find the sum. $n\sum_{n=0}^{\infty}\left(-\frac{3}{8}\right) ^{n}$

A) $811\frac{8}{11}$
B) $314\frac{3}{14}$
C) $58\frac{5}{8}$
D) $85\frac{8}{5}$
E) $35\frac{3}{5}$