Most Important Selected Qs for JEE AdvancedMathematicsInverse Trigonometric Functions

The value of 3 _ n=1 ^ ( 1 _ k=1 ^ ⁻¹ (1+2 _ r=1 ^k r^3 ) )^n is less than:

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Correct answer

D. 4

Step-by-step solution

T=3 _ n=1 ^ ( 1 _ k=1 ^ ⁻¹ (1+2 _ r=1 ^k r^3 ) _ J )^n (1) _ r=1 ^k r^3= ( k(k+1) 2 )^2 (2) ⁻¹ x= ⁻¹ ( 1 x ) aligned & J= 1 ( _ k=1 ^ ⁻¹ ( 1 1+k(k+1) ) )= 1 ( _ k=1 ^ ⁻¹(k+1)- ⁻¹ k ) & 1 ( 2 - 2 )= 1 4 aligned T=3 _ n=1 ^ ( 1 4 )^n Infinite G.P. =3 ( 1 / 4 1-(1 / 4) )=1

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