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If tan -1 (1/1+1.2)+tan -1 (1/1+2.3)+.....+tan -1 (1/1+n(n+1))=tan -1 x then find the value of x

If tan-1 (1/1+1.2)+tan-1(1/1+2.3)+.....+tan-1 (1/1+n(n+1))=tan-1x then find the value of x
 

Grade:12

1 Answers

Arun
25750 Points
5 years ago
Dear student
 
we can write nth term Tn = tan^-1 (1 /1+ n(n+1))
 
Tn = tan^-1 (n+1 – n / 1 + n (n + 1))
 
Tn = tan^-1 (n+1) – tan^-1 n
 
Now you can solve this

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