Evaluating a Finite Sum to a Closed Form Expression

[aaaa202]

I have a finite sum of the form:

∑_n=1^Nexp(an+b√(n))

Is there any trick to evalute this sum to a closed form expression? e.g. like when a finite geometric series is evaluated in closed form.

 

[haruspex]

I have a finite sum of the form:

∑_n=1^Nexp(an+b√(n))

Is there any trick to evalute this sum to a closed form expression? e.g. like when a finite geometric series is evaluated in closed form.

Not here.
You can often get a clue by treating a sum as an integral. In this case you can break it into a difference of two integrals. The first corresponds to ∑_n=1^Nexp(an), which is simply the sum of a geometric series, but the second becomes constant*∫e^ax2.dx.