Prove 10th by mathatical induction
Asked by lovemaan5500 | 2nd Feb, 2019, 08:24: PM
n < 2n for all n N
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
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
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