Home
Class 12
MATHS
Using mathematical induction , prove tha...

Using mathematical induction , prove that `tan^(-1)((1)/(3))+tan^(-1)((1)/(7))+.....+tan^(-1)((1)/(n^2+n+1))=tan^(-1)((n)/(n+2))`

A

`tan^(-1)((n)/(n+2))`

B

`tan^(-1)((2n)/(n+2))`

C

`tan^(-1)((3n)/(n+2))`

D

`tan^(-1)((n)/(n+4))`

Text Solution

Verified by Experts

The correct Answer is:
A
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PRINCIPLE OF MATHEMATICAL

    AAKASH INSTITUTE ENGLISH|Exercise Section-D:(Assertion-Reason Type Questions)|11 Videos
  • PRINCIPLE OF MATHEMATICAL

    AAKASH INSTITUTE ENGLISH|Exercise Section-B((Objective Type Questions (One option is correct))|20 Videos
  • PERMUTATIONS AND COMBINATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section-J (Aakash Challengers Questions)|7 Videos
  • PROBABILITY

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION-J (aakash challengers questions)|11 Videos

Similar Questions

Explore conceptually related problems

Prove that: 2tan^(-1)(1/2)+tan^(-1)(1/7)=tan^(-1)((31)/(17))

Prove that: tan^(-1)(m/n)+tan^(-1)((n-m)/(n+m))=pi/4

Prove that: 2tan^(-1)(1/2)+tan^(-1)(1/7)=tan^(-1)(31/17)

Use principle of mathematical induction to prove that (1+(3)/(1))(1+(5)/(4))...(1+(2n+1)/(n^(2)))=(n+1)^(2)

Prove that: tan^(-1)(2/11)+tan^(-1)(7/24) = tan^(-1)(1/2)

Prove that: tan^(-1)(1/5)+tan^(-1)(1/7)+tan^(-1)(1/3)+tan^(-1)(1/8)=pi/4

Prove that : tan^(-1)(1/5)+tan^(-1)(1/7)+tan^(-1)(1/3)+tan^(-1)(1/8)=pi/4

Prove that: 2tan^(-1) {1/2}+tan^(-1) {1/7}=tan^(-1) {(31)/(17)}

Using mathematical induction, prove that (1)/(1.3.5) + (2)/(3.5.7) +….+(n)/((2n-1)( 2n+1) ( 2n+3)) =( n(n+1))/( 2(2n+1) (2n+3))

Prove the following: 2\ tan^(-1)(1/5)+tan^(-1)(1/8)= tan^(-1)(4/7)