let P(k)=S(k)S(k+1)
then we have
P(k)=S(k)*[S(k1)3/S(k)]
P(k)=S(k1)S(k)3
P(k)=P(k1)3
with P(0)=S(0)*S(1)=37*72=2664
thus
P(k)=26643k
now when P(k)=3 then we have
3=S(k)S(k1)3
S(k)S(k1)=0
thus one of S(k) or S(k1) is zero
so we have P(n)=3
26643n=3
3n=2667
n=889
so either S(888) or S(889) is zero
assume S(888)=0
then S(889)=S(887)3/S(888)
which results in division by zero
thus S(889) is undefined
but if S(889) is undefined then so is P(889)=S(889)*S(890)
contradiction
thus S(888) is not zero and thus S(889) is zero

Posted by Daniel
on 20160128 09:23:03 