Show by using principle of mathematical induction, prove that:

1 + 2 + 3 + -----+ n =

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

Expert Answer:

Let the given statement is P(n)  
P(n) = 1 + 2 + 3 + --- + n =  
For n = 1,   P(1) = is true, since 1 =  
Assume that P(k) is true for some positive integer k, i.e.
1 + 2 + 3 + ---+ k =
We shall prove that P(k +1) is true, whenever P(k) is true.
We have, 1 + 2 + 3 + -----+ k + (k + 1) =   + (k + 1)
                                                              
Thus P(k +1) is true, whenever P(k) is true.
Hence from principle of mathematical induction, the statement P(n) is true for all natural numbers N.

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