Let S denote the infinite sum 2 + 5x + 9x2 + 14x3 + 20x4 + ..., where | x | < 1 and the coefficient of xn-1 is [n(n + 3)]/2, (n = 1, 2, ...). Then S equals:

Let S denote the infinite sum 2 + 5x + 9x² + 14x³ + 20x⁴ + ..., where | x | < 1 and the coefficient of x^n-1 is [n(n + 3)]/2, (n = 1, 2, ...). Then S equals:

A.
(2-x)/(1-x)³
B.
(2-x)/(1+x)³
C.
(2+x)/(1-x)³
D.
(2+x)/(1+x)³

Correct Answer : A

Realated Questions

In a survey of political preference, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one?
Consider the set S = { 1, 2, 3, ... , 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?
A survey was conducted of 100 people to find out whether they had read recent issues of Golmal, a monthly magazine. The summarized information regarding readership in 3 months is given below:
Only September: 18;
September but not August: 23;
September and July: 8;
September: 8; July: 48;
July and August: 10;
none of the three months: 24;
What is the number of surveyed people who have read exactly two consecutive issues (out of the three)?