proof Q: a(n)<=c*a(n-1) for n=>2 for a certain given c>0

[transgalactic]

i am given a real and positive number a1 a2 a3 ...
which goes by a(n)<=c*a(n-1) for every n=>2 for a certain given number c>0 .

prove that
a(n)<=a(1)*c^(n-1)

??

a(n) is the n'th number of the series

 

[Deleted member 4993]

Re: a proof question..

i am given a real and positive number a1 a2 a3 ...
which goes by a(n)<=c*a(n-1) for every n=>2 for a certain given number c>0 .

prove that
a(n)<=a(1)*c^(n-1)

??

a(n) is the n'th number of the series

Try proof by induction - and show your work indicating exactly where you are stuck. That will tell us where we should begin to help you.

 

[transgalactic]

Re: a proof question..

for n=2
i get
a(2)=c*a(1)

this base case doesnt prove anything

??

 

[Deleted member 4993]

Re: a proof question..

what does a(3) look like?

a(3) <= c * a(2)

you have shown

a(2) <= c * a(1)

then

a(3) <= c* c* a(1)

a(3) <= c^2 * a(1)

a(3) <= c^(3-1) * a(1)

Now continue.....

 

[transgalactic]

Re: a proof question..

in a normal base case i should have a resolt such as
1<2
something obvious but here
i get the expression a(3) <= c^(3-1) * a(1)

i dont know whats the values of a(1) and of a(3)
so i dont know if its true

 

[Deleted member 4993]

Re: a proof question..

in a normal base case i should have a resolt such as
1<2
something obvious but here
i get the expression a(3) <= c^(3-1) * a(1)

i dont know whats the values of a(1) and of a(3)<<< You are not reading your question properly - it was derived from the given a[sub:1y5p19x9]n[/sub:1y5p19x9] <= c*a[sub:1y5p19x9]n-1[/sub:1y5p19x9] - so it must be true

so i dont know if its true