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## Homework Statement

I am solving some convolutions, and i have come to these solutions.

a)[tex]\sum[/tex]2

^{k}, summing from -[tex]\infty[/tex] to -1

b)[tex]\sum[/tex]2

^{k}, summing from -[tex]\infty[/tex] to n , where n <=-1

## Homework Equations

the geometric series summation formula, from 0 to N

[tex]\sum[/tex]a

^{k}= 1-a

^{N+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?