×

#### Thank you for registering.

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

Click to Chat

1800-1023-196

+91-120-4616500

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
```
Find sum of infinite terms of series cot^-1(2^2+1/2)+cot^-1(2^3+1/4)+cot^-1(2^4+1/8)............

```
2 years ago

## Answers : (1)

2074 Points
```							We know that arccotx=arctan (1/x) for x greater than zero. So we convert all terms into arctan. Now the nth term isarctan (2^n/1+2^n*2^n+1)= arctan (2^n+1-2^n/1+2^n*2^n+1)= arctan 2^n+1-arctan2^nBut the above sum telescopes.So sum is arctan infinite-arctan2=pi/2-arctan2= arccot2
```
2 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

## Other Related Questions on Trigonometry

View all Questions »

### Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution

### Course Features

• 31 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions