The sum to infinity of the series 1 + 2/3 + 6/3^2 + 10/3^3

• Sequences Series

The sum to infinity of the series 1 + 2/3 + 6/3² + 10/3³ + ... is

1. 2
2. 3
3. 4
4. 6

Answer

Let S = 1 + 2/3 + 6/3² + 10/3³ + ...

S/3 = 1/3 + 2/3² + 6/3³ + ..

S - S/3 = 1 + 1/3 + 4/3² + ...

2S/3 = 4/3 + 4/3²/(1 - 1/3)

= 4/3 + 2/3

The correct option is B.