Find the value of the limit of the sequence defined by:
a(sub 1)=1
a (sub n+1)=13-(1/a(sub n))
I have no idea how to do that.
Find the value of the limit of the sequence defined by:
a(sub 1) = Square root of 10
a(sub n+1) = Square root of (10+a(sub n))
This one either. These are the only two out of 30 that I couldn't do. He said they'd be on the test so I need to learn... bummer.
The first sequence
I'll post the proof that exists
First we'll show that: if
By induction:
is true
Assume holds then we'll prove that:
then
so: and then: which completes the first part
so it is a positive sequence and therefore it is bounded by 13 since
This shows that the sequence is incresing and for all , thus it converges to say
LIMIT:
Since taking the limit on both sides: then now find the roots of this equation and remember that to see which one is the limit.