Most Important Selected Qs for JEE AdvancedMathematicsInverse Trigonometric Functions
The value of the expression ( ⁻¹ ( 1 2 )+ ⁻¹ ( 2 9 )+ ⁻¹ ( 1 8 )+ ⁻¹ ( 2 25 )+ ⁻¹ ( 1 18 )+ ) , is:
Correct answer
3
Step-by-step solution
Let S= ⁻¹ ( 1 2 )+ ⁻¹ ( 2 9 )+ ⁻¹ ( 1 8 )+ ⁻¹ ( 2 25 )+ ⁻¹ ( 1 18 )+ aligned & = ⁻¹ ( 2 4 )+ ⁻¹ ( 2 9 )+ ⁻¹ ( 2 16 )+ ⁻¹ ( 2 25 )+ ⁻¹ ( 2 36 )+ T_n & = ⁻¹ ( 2 (n+1)^2 ) S & = _ r=1 ^ ⁻¹ ( 2 r^2+2 r+1 )= _ r=1 ^ ⁻¹ ( (r+2)-r 1+r(r+2) )= _ r=1 ^ ⁻¹(r+2)- ⁻¹(r) S & = _ n ⁻¹ ( 3 n^2+7 n n^2+9 n+10 )= ⁻¹(3) aligned Hence, S= ( ⁻¹ 3 )=3