Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

What is the sum of the infinite series; cot^-1(2)+cot^-1(8)+cot^-1(18)+cot^-1(32)+.......infinity ?

What is the sum of the infinite series;
cot^-1(2)+cot^-1(8)+cot^-1(18)+cot^-1(32)+.......infinity ?

Grade:12th pass

1 Answers

Vishal Kumar
26 Points
3 years ago
firstly in such questions try to find pattern between numbers : here it is 2n and then try to express it in form of tan-1a – tan-1b
∑ cot-1 ( 2n)  = ∑ tan-1 ( 1/2n)   { from n=1 to infinity }
tan-1 ( 2/4n)  =  tan-1 { (2n+1) – (2n - 1) \1 + (2n - 1)(2n+1)  } …......................1
tan-1a - tan-1b = tan-1 {(a-b)/1 + a*b}
so equation 1 equals to tan-1 (2n+1) – tan-1 (2n-1)
 so now the qauestion is ∑ {tan-1 (2n+1) – tan-1 (2n-1) }   [ n from 1 to infinity]
so now the answer is  ( \pi/2 – \pi/4 ) = \pi/4 

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free