How do you find the sum of the infinite geometric series given #1-0.5+0.25-...#?

1 Answer
Oct 23, 2016

Sum of the infinite geometric series is #2/3#.

Explanation:

As #-0.5/1=0.25/-0.5=-1/2#, the series #1-0.5+0.25-.......# is a geometric series, whose first term #a=1# and common ratio #r=-1/2# and #|r|<1#.

In a geometric series where first term is #a# and common ratio is #|r}<1#, sum up to #n^(th)# term #S_n# is given by

#S_n=(a(1-r^n))/(1-r)# and as in such infinite series as #n->oo#, the sum tends to #S=a/(1-r)#

Hence, here sum of the infinite geometric series #1-0.5+0.25-.......# is

#S=1/(1-(-1/2))=1/(1+1/2)=1/(3/2)=2/3#