If  P(n) is the statement 72n + 23n - 3.3n - 1 is divisible by 25 for all n N, then what is P(k + 1)?

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

Expert Answer:

We note that P(n) is true for n=1,since 72 +1=50 ,which is divisible by 25.
Assume that P(k) is true i.e +=25d,when d
We will prove P(k+1) is true whenever P(k)is true.
P(k+1)=+
          =72[+ -]+
          =[25d-]+
          =x25d + 50x
          =25(+2x)
          =25r
the expression is divisible by 25.
Thus,P(k+1) is true whenever P(k) is true.

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