Dave the mischievous astronomer

Calculus Level 3

Dave is very mischievous. He presents Carl a problem:

Take the function \[f(n)=\sum^n_{k=0}\log\left(\frac{k+2}{k+3}\right)\] What is \(f(-2)\)?

Carl immediately studies the problem carefully. After some thought he tells Dave that it cannot be done. "You cannot have a smaller upper limit on the summation! This is ludicrous!".

Dave replies with a smile "Ah! But to the eyes of an astronomer, the problem can be solved!".

Can you help Carl solve Dave's problem?


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