Possibly an infinite sequence of logs

zzinfinity

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Nov 12, 2009
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Let a and b be natural numbers with a < b. Simplify:

log2a(2a+1) * log2a+1(2a+2) * log2a+3(2a+3) .... log2b-1(2b)



I have an engineering degree but am still completely stumped on this. Any one have a suggestion?
 
Let a and b be natural numbers with a < b. Simplify:

log2a(2a+1) * log2a+1(2a+2) * log2a+3(2a+3) .... log2b-1(2b)



I have an engineering degree but am still completely stumped on this. Any one have a suggestion?

Is that term correct?
 
Assuming that the corrected sequence is:

log2a(2a+1) * log2a+1(2a+2) * log2a+2(2a+3) .... log2b-1(2b)


Use the fact that

\(\displaystyle log_u(v) = \dfrac{log_u(w)}{log_v(w)} \)

The sequence will telescope.
 
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