Re: sum of recursive fn: solving for n

*To*: mathgroup at smc.vnet.net*Subject*: [mg22130] Re: [mg22108] sum of recursive fn: solving for n*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Wed, 16 Feb 2000 02:34:47 -0500 (EST)*References*: <200002140703.CAA12423@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

fiona wrote: > > what am i doing wrong here? > > f[x_] := (f[x-1])*2 > f[1] =2 > Solve[Sum[f[x], {x, 1,n}] ==62, n] > > tia, > fiona For one thing, Sum cannot handle this symbolic summation. In[32]:= Sum[f[x], {x,1,n}] $RecursionLimit::reclim: Recursion depth of 256 exceeded. $RecursionLimit::reclim: Recursion depth of 256 exceeded. $RecursionLimit::reclim: Recursion depth of 256 exceeded. General::stop: Further output of $RecursionLimit::reclim will be suppressed during this calculation. Out[32]= Sum[2894802230932904885589274625217197696331749616641014100986439600\ > 1978282409984 Hold[f[(-253 + x) - 1]], {x, 1, n}] One way to attack the problem is to first solve the recurrence in closed form. In[33]:= <<DiscreteMath`RSolve` In[35]:= soln = RSolve[{g[x]==2*g[x-1], g[1]==2}, g[x], x] x Out[35]= {{g[x] -> 2 }} Now obtain a symbolic form of the sum. In[39]:= h[n] = Sum[g[x]/.soln[[1,1]], {x,1,n}] n Out[39]= 2 (-1 + 2 ) In[40]:= Solve[h[n]==62, n] Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found. Out[40]= {{n -> 5}} Daniel Lichtblau Wolfram Research