Prove by using the principle of mathematical induction 3n < 4n for all n N.

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

Let P(n): 3n < 4n  for all n  N.
P(1): 3 < 4, which is true. Thus P(n) is true for n = 1.
Let P(k) be true for some natural number k
i.e. 3k < 4k
Now we prove that P(k +1) is true whenever P(k) is true.
Thus P(k +1) is true whenever P(k) is true.
By principle mathematical induction 3n < 4n for all n  N.  

Answered by  | 4th Jun, 2014, 03:23: PM