Most Important Selected Qs for JEE AdvancedMathematicsSequences and Series

Let be a sequence such that T_n^3+2 T_n=T_ n+1 n N , and T₁=1 , then:

Options

A_ n=1 ¹⁰⁰ (T_n^3+T_n+1 )=T₁₀₁+99
B_ n=1 ¹⁰⁰ (T_n^3+T_n+1 )=T₁₀₁+100
C_ n=1 ¹⁰⁰ (T_n^2+2 )=T₁₀₀
D_ n=1 ¹⁰⁰ ( T_ n+1 T_n -T_n^2 )=2¹⁰⁰

Correct answer

D. _ n=1 ¹⁰⁰ ( T_ n+1 T_n -T_n^2 )=2¹⁰⁰

Step-by-step solution

(1) aligned & T_n^3+T_n+1=T_ n+1 -T_n & _ n=1 ¹⁰⁰ (T_n^3+T_n+1 )=T₁₀₁-T₁+100=T₁₀₁+99 aligned (2) aligned & T_n^2+2= T_ n+1 T_n & _ n=1 ¹⁰⁰ (T_n^2+2 )= _ n=1 ¹⁰⁰ T_ n+1 T_n = T₁₀₁ T₁ =T₁₀₁ aligned (4) _ n=1 ¹⁰⁰ ( T_ n+1 T_n -T_n^2 )=2¹⁰⁰

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