How do you find the sum of the infinite geometric series 4 - 2 + 1 – 1/2 + . . .?

Question

5561 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-21T08:42:38

#8/3#

#a_2/a_1=(-2)/4=-1/2#

#a_3/a_2=1/-2=-1/12#

#implies# common ratio#=r=-1/2# and first term#=a_1=4#

Sum of infinite geometric series is given by

#Sum=a_1/(1-r)#

#implies Sum=4/(1-(-1/2))=4/(1+1/2)=8/2+1=8/3#

#implies S=8/3#

Hence the sum of the given given geometric series is #8/3#.