Question

Let 'S_n' denotes the sum of 1^st 'n' terms of an A.P. Then the value of S = $\lim _ { x \rightarrow \infty }$ $\sum_{r = n}^{\infty}\frac{f(r)}{n}$, where f(n) = $\frac{S(3n)}{S(2n) - S(n)}$

• A. 3
• B. 1/3
• C. 9
• D. None of these

Answer 1

Answer: (A)

3

Answer 2

S(3n) = $\frac{3n}{2}$ [2a + (3n –1) d]

S (2n) = $\frac{2n}{2}$ [2a + (2n –1) d]

S(n) = $\frac{n}{2}$ [2a + (n –1) d]

\ S(2n) –S(n) = $\frac{n}{2}$ [2 (2a + $\overline{2n - 1}$ d) –2a – (n –1)d] = $\frac{n}{2}$

[2a + (3n –1) d] = $\frac{S(3n)}{3}$

\ $\frac{S(3n)}{S(2n) - S(n)}$= 3 = f(n)