Solving for Sum element

*To*: mathgroup at smc.vnet.net*Subject*: [mg27260] Solving for Sum element*From*: Ben Jacobson <bjacobson at illumitech.com>*Date*: Wed, 14 Feb 2001 03:41:27 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

I want to solve for one element in an equation involving long sums. The actual equation is of course complicated, but a very simplified example would be Sum[a[i],{i,0,n}]==x where I want to solve for a[0]. The solution should be something like a[0]->x-Sum[a[i],{i,1,n}. Solve[Sum[a[i], {i, 0, n}] == x, a[0]] works fine if, for example, n=3, but it returns an empty result for symbolic n. Is there a way to tell Solve to assume that n>1 and to solve accordingly? The best I've been able to do so far is to explicitly remove the element I'm interested in from the sum: In: Solve[a[0] + Sum[a[i], {i, 1, n}] == x, a[0]] Out: {{a[0] -> x - Sum[a[i], {i, 1, n}]}} This works nicely, but becomes awkward when I try to solve for more elements and longer sums. Thanks. Ben Jacobson Illumitech Inc.