Mathematics · 2021
JEE Main · 24 February 2021, Shift 1 · Q90
lim_n → ∞ tan {Σ_r=1^n tan^-1(1/(1+r+r^2))} is equal to \ \ \ \.
$\displaystyle \lim _{n \rightarrow \infty} \tan \left\{\sum_{r=1}^n \tan ^{-1}\left(\frac{1}{1+r+r^2}\right)\right\}$ is equal to \_\_\_\_.
Official answer
1
More from Inverse Trigonometric Functions
- Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x)= sec^-1(2[x]+1) is:2025
- Let x= sin (2 tan^-1 α) and y= sin (1/2 tan^-1 4/3). If S={α ∈ R: y^2=1-x}, then Σ_α ∈ S 16 α^3 is equal to \ \ \ \.2022
- The value of tan^-1((cos ((15 π)/4)-1)/(sin ((π)/4))) is equal to:2022
- If (π)/4+Σ_p=1^11 tan^-1((2^p-1)/(1+2^2 p-1))=α, then tan α is equal to ____.2026
- tan (2 tan^-1 1/5+ sec^-1 (√5)/2+2 tan^-1 1/8) is equal to:2022
- If the domain of the function f(x)=(cos^-1 √(x^2-x+1))/(√(sin^-1((2 x-1)/2))) is the interval (α, β], then α+β is equal to:2021
- For k ∈ R, let the solutions of the equation cos ( sin^-1(x cot ( tan^-1( cos ( sin^-1 x)))))=k, 0<|x|<1/(√2) be α and β, where the inverse…2022
- Let the inverse trigonometric functions take principal values. The number of real solutions of the equation 2 sin^-1 x+3 cos^-1 x=(2 π)/5, is ____.2024
JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.