NTA Abhyas JEE Main2020MathematicsSequences and SeriesPractice
The sum to n terms of 1 1.3 + 2 1.3 . 5 + 3 1.3 . 5.7 + 4 1.3 . 5.7 . 9 + . . . . . . . . is
Options
- A1 2 1 + 1 1.3 . 5 . . . . . . . . 2 n + 1
- B1 2 1 - 1 2.4 . 6 . . . . . . . . 2 n
- C1 2 1 - 1 1.3 . 5 . . . . . . . . 2 n + 1
- DNone of these
Correct answer
C. 1 2 1 - 1 1.3 . 5 . . . . . . . . 2 n + 1
Step-by-step solution
t n = n 1.3 . 5 .   . . . . . . . . . 2 n + 1 =   1 2 .   2 n + 1 - 1 1.3 . 5 .   . . . . . . . . . 2 n + 1 = 1 2 1 1.3 . 5 . . . . . . 2 n - 1 - 1 1.3 . 5 . . . . . . . 2 n + 1 = 1 2 T n - 1 -   T n ∴ 2 t n = T n - 1 -   T n     … 1   w h e r e   T n = 1 1.3 . 5 . . . . . . . 2 n + 1 ∴     2 S n   =   ∑ n = 2 n 2 t n + 2 t 1 ⇒   2 S n   −   2 t 1   =   ( T 1   −