JEE Main20254 Apr 2025Evening ShiftMathematicsInverse Trigonometric FunctionsActual
The sum of the infinite series ⁻¹ ( 7 4 )+ ⁻¹ ( 19 4 )+ ⁻¹ ( 39 4 )+ ⁻¹ ( 67 4 )+ . is :-
Options
- A2 + ⁻¹ ( 1 2 )
- B2 - ⁻¹ ( 1 2 )
- C2 + ⁻¹ ( 1 2 )
- D2 - ⁻¹ ( 1 2 )
Correct answer
D. 2 - ⁻¹ ( 1 2 )
Step-by-step solution
aligned & T _ n = ⁻¹ ( 4 4 n ^2+3 ) & T _ n = ⁻¹ ( ( n + 1 2 )- ( n - 1 2 ) 1+ ( n + 1 2 ) ( n - 1 2 ) ) & T _ n = ⁻¹ ( n + 1 2 )- ⁻¹ ( n - 1 2 ) & T ₁+ T ₂+ + T _ n = ⁻¹ ( n + 1 2 )- ⁻¹ ( 1 2 ) & S _ = 2 - ⁻¹ ( 1 2 ) aligned option (4)