Summation of series

JEE Main Mathematics · Inverse Trigonometric Functions · 3 questions, latest first

• If (π)/4+Σ_p=1^11 tan^-1((2^p-1)/(1+2^2 p-1))=α, then tan α is equal to ____.20265 April, Shift 1 · Q24
• The sum of the infinite series cot^-1(7/4)+ cot^-1(19/4)+ cot^-1(39/4)+ cot^-1(67/4)+…. is:20254 April, Shift 2 · Q13
• Let a_1=1, a_2, a_3, a_4, ….. be consecutive natural numbers. Then tan^-1(1/(1+a_1 a_2))+ tan^-1(1/(1+a_2 a_3))+…..+…202330 January, Shift 2 · Q78