I appear to be having some difficulty with some (admittedly pretty simple sums)..

So..

1. Sum of 1 from i=0 to N: seems easy enough, 1 + N = N+1.

2. Sum of 1 from t=1 to T. T. Now sum it up from k=1 to k=K, and you have.. TK.

3. Now this one is where I'm seemingly having some difficulty:

the sum of 0.5^k from t=1 to t=T is 1 - 2^(-T) (as per the geometric summation formula.) now sum that up from k=1 to K, and we have.. K(sum of 1 from 1 to K) + (2^ (-K) - 1)(as per a reapplication of the geo. sum formula.) I think this is right.. could you guys confirm?

4. Now this is in a similar mold as the last problem - the sum of 0.5^k from t=1 to t=T is 1 - 2^(-T).. but I think that when you sum that from k=1 to inf, it diverges. Is that true?

Thank you.

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