Trigonometric EquationMedium
Question
Let f(n) = tan-1 
+ tan-1 
+ tan-1 
+ .... n terms, then 
f(n) is -
+ tan-1 + tan-1 + .... n terms, then f(n) is - Options
A.less than 
but greater than 
but greater than B.less than
C.greater than
D.equal to
Solution
Tn = tan-1 
= tan-1
Tn = tan-1 ((n + 1) (n + 2)) - tan-1(n(n + 1))
∑ Tn = tan-1(n + 1)(n + 2) - tan-12
f(n) = 
- tan-1 2 = tan-1
√2 - 1 < ⇒ tan-1 (√2 - 1) < tan-1 tan-1 > 
= tan-1
Tn = tan-1 ((n + 1) (n + 2)) - tan-1(n(n + 1))
∑ Tn = tan-1(n + 1)(n + 2) - tan-12
f(n) = - tan-1 2 = tan-1√2 - 1 <
⇒ tan-1 (√2 - 1) < tan-1 tan-1 > Create a free account to view solution
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