Limit of a Sequence

JEE Main Mathematics · Limits · 3 questions, latest first

• Let f(x)= lim_n → ∞ Σ_r=0^n((tan (x / 2^r+1)+ tan^3(x / 2^r+1))/(1- tan^2(x / 2^r+1))). Then lim_x → 0 (e^x-e^f(x))/((x-f(x))) is…202528 January, Shift 2 · Q24
• lim_n → ∞{(2^(1/2)-2^(1/3))(2^(1/2)-2^(1/5)) … …(2^(1/2)-2^(1/(2 n+1)))} is equal to20236 April, Shift 2 · Q9
• The value of lim_n → ∞ (1+2-3+4+5-6+… …+(3 n-2)+(3 n-1)-3 n)/(√(2 n^4+4 n+3)-√(n^4+5 n+4)) is:202325 January, Shift 1 · Q65