NTA Abhyas JEE Main2020MathematicsSequences and SeriesPractice
Let f n = ∑ r = 1 10 n 6 + r d and g n = ∑ r = 1 n 6 + r d , where n ∈ N ,   d ≠ 0 . If f n g n is independent of n , then d is equal to
Options
- A12
- B- 6
- C6
- D- 12
Correct answer
D. - 12
Step-by-step solution
f n g n = 60 n + 5 n 10 n + 1 d 6 n + n n + 1 2 d = 5 12 + d n + 50 n 2 d 6 + d 2 n + n 2 d 2 If d = - 12 , f n g n = 100