For any natural number n, Prove that

.

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

Expert Answer:

The proof is obtainted by applying principle of mathematical induction.
Let the given statement be
P(n): 
For n = 1, we have
P(1) :
Thus P(1) is true.
Suppose P(k) is true for some positive integer k, i.e.
                               (1)
We shall prove that P(k+1) is also true, i.e.
Now,
= (a+b)  
 
[From (1)]   
                                                                                                       (By actual multiplication)
                                                                                                         [grouping like terms]
    
 Thus, it has been proved that P(k +1) is true whenever P(k) is true.
 By principle of mathematical induction, P(n) is true for every positive integer n.

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