# Evaluating a sum

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#1
Evaluate the sum

I've tried rewriting the sum by splitting terms so that , as the first sum just converges to 2, but I can't seem to really do much else with the second sum.

Is there a better way that I could split this sum to make the problem more manageable?
Last edited by username53983805; 1 month ago
0
1 month ago
#2
Evaluate the sum

I've tried rewriting the sum by splitting terms so that , as the first sum just converges to 2, but I can't seem to really do much else with the second sum.

Is there a better way that I could split this sum to make the problem more manageable?
What do you notice about the numerator and denominator of the original sequence?
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#3
(Original post by mqb2766)
What do you notice about the numerator and denominator of the original sequence?
Numerator is fibonacci, denominator is increasing powers of two
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1 month ago
#4
Numerator is fibonacci, denominator is increasing powers of two
So think how you can use that info.

As a hint, you can "prove" the standard result of
S = 1 + 1/2 + 1/4 + 1/8 + ... = 2
by noting
S = 1 + S/2
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#5
(Original post by mqb2766)
So think how you can use that info.

As a hint, you can "prove" the standard result of
S = 1 + 1/2 + 1/4 + 1/8 + ... = 2
by noting
S = 1 + S/2
I now have something.

So

.
Last edited by username53983805; 1 month ago
0
1 month ago
#6
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