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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 | 04 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 | 04 Jun, 2014, 03:23: PM
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