       Re: Summations

• To: mathgroup at smc.vnet.net
• Subject: [mg78302] Re: Summations
• From: dimitris <dimmechan at yahoo.com>
• Date: Thu, 28 Jun 2007 04:17:28 -0400 (EDT)
• References: <f5qme1\$46g\$1@smc.vnet.net>

```
Sima       :
> Can someone please solve this summations:
>
> Summation(from i=1 to n) (i * a ^ i)
>
> Summation(from i=1 to m) (i * n ^ i + n ^ 3)
>
> you can mail me sollutions. Thanks

Hi.

This is not the proper place for
posting messages like the current one.
Try...

http://www.artofproblemsolving.com/

Anyway...

In Mathematica your sums can be evaluated with the
command Sum.
I don't know your level of knowledge in Mathematica, but
since you seem you don't care, I don't try to explain anything.

In:=
sum1 = Sum[i*a^i, {i, 1, n}]
sum2 = Sum[i*n^i + n^3, {i, 1, m}]

Out=
(a*(1 - a^n - a^n*n + a^(1 + n)*n))/(-1 + a)^2

Out=
m*n^3 + (n*(1 - n^m - m*n^m + m*n^(1 + m)))/(-1 + n)^2

Dimitris

```

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