Sequence And Series Question 468

Question: The sum can be found of a infinite G.P. whose common ratio is $ r $

[AMU 1982]

Options:

A) For all values of $ r $

B) For only positive value of $ r $

C) Only for $ 0<r<1 $

D) Only for $ -1<r<1(r\ne 0) $

Show Answer

Answer:

Correct Answer: D

Solution:

$ {S_{\infty }}=\frac{a}{1-r} $ where $ -1<r<1\ \ i.e.\ |r|\ <1 $ .



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