Find-the-sum-of-the-first-nterms-of-the-G-P-3-1-1-3-and-show-that-the-sum-cannot-exceed-9-2-however-great-n-may-be-

Question Number 46697 by KMA last updated on 30/Oct/18

F i n d t h e s u m o f t h e f i r s t n t e r m s

o f t h e G . P 3 + 1 + \frac{1}{3} + \dots a n d s h o w t h a t

t h e s u m c a n n o t e x c e e d \frac{9}{2} h o w e v e r

g r e a t n m a y b e .

Answered by Joel578 last updated on 30/Oct/18

S_{n} = \frac{a (1 - r^{n})}{1 - r} = \frac{3 (1 - {(\frac{1}{3})}^{n})}{1 - \frac{1}{3}}

= \frac{9}{2} (1 - {(\frac{1}{3})}^{n})

\lim_{n \to \infty} S_{n} = \lim_{n \to \infty} [\frac{9}{2} (1 - {(\frac{1}{3})}^{n})]

= \frac{9}{2} . \lim_{n \to \infty} (1 - {(\frac{1}{3})}^{n})

= \frac{9}{2} (1 - 0)

= \frac{9}{2}

It is showed that as n goes larger and larger,

its value getting closer to \frac{9}{2} and never exceed \frac{9}{2}

Facebook Tweet Pin