Sequences and Series

JEE Main Mathematics · Progressions · 4 questions, latest first

• If Σ_k=1^n a_k=6 n^3, then Σ_k=1^6((a_k+1-a_k)/36)^2 is equal to ____.20262 April, Shift 1 · Q22
• Let a_1=1 and for n ≥ 1, a_n+1=1/2 a_n+(n^2-2 n-1)/(n^2(n+1)^2). Then |Σ_n=1^∞(a_n-2/n^2)| is equal to ____.202621 January, Shift 1 · Q22
• Let <a_n> be a sequence such that a_0=0, a_1=1/2 and 2 a_n+2=5 a_n+1-3 a_n, n=0,1,2,3, …. Then Σ_k=1^100 a_k is equal to202528 January, Shift 1 · Q5
• Let <a_n> be a sequence such that a_1+a_2+…+a_n=(n^2+3 n)/((n+1)(n+2)). If 28 Σ_k=1^10 1/a_k=p_1 p_2 p_3 … p_m, where p_1, p_2,…202312 April, Shift 1 · Q8