Show that if statement P(n): 2 + 4 + 6 + --- + 2n =  n( n + 1) + 2 is true for n = k, then it is also true for n = k + 1. Can we apply the principle of mathematical induction?

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

Expert Answer:

P (n): 2 + 4 + 6 + --- + 2n = n(n + 1) + 2 
We are given that P(k) is true.
i.e. 2 + 4 + 6 + --- + 2k = k(k + 1) + 2
P(k + 1): k(k+ 1) + 2 + 2(k +1) = (k + 1)(k + 2) + 2
To apply the principle of mathematical induction we will check whether P(1) is true or not.
P(1): 2 = 1 (1 + 1) + 2, which is not true.
Since P(1) is not true, we cannot apply the principle of mathematical induction.

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