The sum of the infinite series cot^-1 ⁡ ( 74 )+ cot^-1 ⁡ ( 194 )+ cot^-1 ⁡ ( 394 ) is:

Question

Accepted Answer

Correct answer: C. (c) cot^-1 ( 74 )+ cot^-1 ( 194 )+ cot^-1 ( 394 )+ cot^-1 ( 674 )+ … . . T_r= cot^-1 ( 4r^2+34 ) T_r= tan^-1 ( 1( 34+r^2) ) T_r= tan^-1 ( (r+ 12)-(r- 12)1+r^2- 14 ) T_r= tan^-1 ( (r+ 12)-(r- 12)1+(r+ 12)(r- 12) ) T_r= tan^-1(r+ 12)- tan^-1(r- 12) T_1= tan^-1 ( 32 )- tan^-1 ( 12 ) T_2= tan^-1 ( 52 )- tan^-1 ( 32 ) . . . . . . . . . T_n= tan^-1 ⁡ ( 2n+12 )- tan^-1 ⁡ ( 12 ) T_r= tan^-1 ⁡ ( 2n+12 )- tan^-1 ⁡ ( 12 ) T_r= 2- tan^-1 ⁡ ( 12 )

$The sum of the infinite series cot^{- 1} (\frac{7}{4}) + cot^{- 1} (\frac{19}{4}) + cot^{- 1} (\frac{39}{4}) is:$

Solution

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