If 1 + x + x^2 + x^3 + ............upto infinite = 2 then x^3 + x^4 + x^5 + ............upto infini

M4maths Previous Puzzles

26 Apr 2012 INFINITE SEQUENCE

If 1 + x + x^2 + x^3 + ............upto infinite = 2
then x^3 + x^4 + x^5 + ............upto infinite = ?

OPtion

1) 1/2
2) 1
3) 1/4
4) 1/8
5) 1/16
6) 1/32
7) 1/10
8) 1/3
9) 1/6
10) none of these

Solution

for infinite multiplicative sequence (G. P.)
formula for getting sum = a/(1-r)
here a is first term and r is ratio of second and first term.
so on solving by formula x = 1/2
so ? = 2 - 1 - 1/2 - 1/4 = 1/4

Correct Option: 3 Best Solution (0)