## Quant Question Of The Day : 14

[Latexpage]

# Algebra

Find the sum of infinite numbers of the set S ∈ {1,1/2,1/3,1/4,1/6,1/8,1/9,1/12,1/16,..}. It is given that each term in S is of the form 1/(2^{a} ×3^{b} ) where a, b are non-negative integers.

1. 2

2. 3

3. 4

4. infinite

### Solve our previous ‘questions of the day’

1.Quant Question Of The Day : 13

2. Quant Question Of The Day : 12

3. Quant Question Of The Day : 11

Answer is 3.

The given series is a product of two infinite series: (1+1/2+1/4+…..).(1+1/3+1/9+1/81+. .)= 2.(3/2)=3

Option 2.

3

Approach:

The above series is a product of 2 infinte GP.

Also,

1/2^a*3^b can be expanded as

1/2^0*3^0 + 1/2^1*3^0 + 1/2^0*3^1 + 1/2^1*3^1 +….

Which is nothing but equal to

1+1/2+1/3+1/6+….

as a and b values are increased the sequence will increase.

The above series is actually a product of two gp’s

(1+1/2)(1+1/3) = 1+1/2+1/3+1/6…. Which is the same equation.

Hence we can find

GP sum = a/1-r

2*3/2=3