I am solving some convolutions, and i have come to these solutions.
a)[tex]\sum[/tex]2k, summing from -[tex]\infty[/tex] to -1
b)[tex]\sum[/tex]2k, summing from -[tex]\infty[/tex] to n , where n <=-1
the geometric series summation formula, from 0 to N
[tex]\sum[/tex]ak = 1-aN+1 / 1-a , summing from 0 to N
The Attempt at a Solution
Is there a direct formula to simplify the sums i've come to?I mean a formula for any summation bounds, not just for "from zero to N" format.Moreover, can i plug in infinity to the formula mentioned above?
I understand that i can break up the sum and/or flip the sum bounds any way that i like, correct?