Plz help on these:
(a) Prove by mathematical induction that
is divisible by 43 for each positive integer n
(b) Show that for using mathematical induction method.
Thnx in advance.
this one is not that bad, in fact, i think giving you a hint would give the answer away anyway, so let's just do it.
we wish to prove the statement:
for all
Now, which is true. So the inductive step is complete.
Assume is true for some , we show is true. that is, we want to show
now,
.....since
......since
thus we have shown is true.
Thus we have proven by induction