 ×     #### 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
```
Prove that 2n > n for all positive integers n by the Principle of Mathematical Induction
Prove that 2n > n for all positive integers n by the Principle of Mathematical Induction

```
4 months ago Anand Kumar Pandey
2937 Points
```							Welcome to askIITiansAssume that P(n): 2n> nIf n =1, 21>1. Hence P(1) is trueLet us assume that P(k) is true for any positive integer k,It means that, i.e.,2k> k …(1)We shall now prove that P(k +1) is true whenever P(k) is true.Now, multiplying both sides of the equation (1) by 2, we get2. 2k> 2kNow by using the property,i.e., 2k+1> 2k = k + k > k + 1Hence, P(k + 1) is true when P(k) is true.Therefore, P(n) is true for every positive integer n is proved using the principle of mathematical induction.Thanks
```
4 months ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Analytical Geometry

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

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