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Question Number 203357 by Calculusboy last updated on 17/Jan/24

F o r t h e s e r i e s 5 - \frac{5}{2} + \frac{5}{4} - \frac{5}{8} + \cdot \cdot \cdot + \frac{{(- 1)}^{n - 1} 5}{2^{n - 1}}

f i n d a n e x p r e s s i o n f o r t h e s u m o f t h e f i r s t

n t e r m s . A l s o i f t h e s e r i e s c o n v e r g e s,

f i n d t h e s u m t o \infty .

Answered by mr W last updated on 17/Jan/24

G . P . w i t h q = - \frac{1}{2}

S_{n} = \frac{5 (1 - {(- \frac{1}{2})}^{n})}{1 - (- \frac{1}{2})} = \frac{10}{3} [1 - \frac{{(- 1)}^{n}}{2^{n}}]

\lim_{n \to \infty} S_{n} = \frac{10}{3}

Commented by Calculusboy last updated on 17/Jan/24

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