Sequences Question

[mrugby]

Hi,
I am stuck on this maths Q.

I have made an attempt (attached below). I think the sequence converges to a number around 2. Please can someone help/show me how I would get to this answer?


Thanks!

 

[Dr.Peterson]

Don't look at the sum; look at the terms you are adding! Do you see how your 6th line compares to your 1st?

Also, pay attention to the rule for the numerators in T, which is the reason for the relationship you should see.

 

[mrugby]

Don't look at the sum; look at the terms you are adding! Do you see how your 6th line compares to your 1st?

Also, pay attention to the rule for the numerators in T, which is the reason for the relationship you should see.

Hi,
The numerators follow a fibonacci sequence, the denominators follow a geometric sequence of the form 0.5*0.5^(n-1).
Should the numerators of 3/4T continue to follow the fibonacci sequence?
Please could you give me a tip on how to find the value of T given this knowledge?
Thanks

 

[Dr.Peterson]

Hi,
The numerators follow a fibonacci sequence, the denominators follow a geometric sequence of the form 0.5*0.5^(n-1).
Should the numerators of 3/4T continue to follow the fibonacci sequence?
Please could you give me a tip on how to find the value of T given this knowledge?
Thanks

Do you see WHY the numerators of the summation for 3/4 T follow the Fibonacci sequence? There is a reason, but if you don't see it, then you can't assume it. Here's a hint:



Do you then see that 3/4 T consists of all the terms of the summation for T except the first? Therefore 3/4 T = T - 1/2. That's the relationship I suggested you'd see.