Solve for the sum of the infinite geometric series 1+1/3+1/9+1/27+...

Answer 1

S = a / (1 - r)

S = 1 / (2/3)

S = 3 / 2

Answer 2

3/2 = 1.5 = 1 1/2 = the sum = S

S = 1 +1/3 + 1/9 + ...

multiply by 1/3

S/3 = 1/3+1/9+....

subtract

S-S/3 = 1 (all the other terms cancel out)

3S/3- S/3=1

(3-1)S/3=1

2S/3 = 1

S = 3/2 x 1 = 3/2 = the sum of the geometric series

or use the general formula for the sum of an infinite series

S= a/(1-r) where r >1

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

S =3/2= 1.5