Prove 10th by mathatical induction

Asked by lovemaan5500 | 2nd Feb, 2019, 08:24: PM

Expert Answer:

n < 2n for all n begin mathsize 16px style element of end styleN
Consider, n = 1 we get
1 < 21 which is true.
Let us assume that n < 2n is true for k. Hence, k < 2k
We will prove this for k + 1.
To show that k + 1 < 2k + 1
We have 
 k < 2k
2k < 2 × 2k 
k + k < 2k + 1
As k + 1 ≤ 2k + 1
k + 1 < 2k + 1
By mathematical induction n < 2n for all natural numbers.


Answered by Sneha shidid | 4th Feb, 2019, 11:22: AM