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[98]:= sum1 = Sum[i*a^i, {i, 1, n}] sum2 = Sum[i*n^i + n^3, {i, 1, m}] Out[98]= (a*(1 - a^n - a^n*n + a^(1 + n)*n))/(-1 + a)^2 Out[99]= m*n^3 + (n*(1 - n^m - m*n^m + m*n^(1 + m)))/(-1 + n)^2 Dimitris