#### Thank you for registering.

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

Click to Chat

1800-5470-145

+91 7353221155

CART 0

• 0
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 ?

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