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MathGroup Archive 2000

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Re: sum of recursive fn: solving for n

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22111] Re: [mg22108] sum of recursive fn: solving for n
  • From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
  • Date: Wed, 16 Feb 2000 02:34:27 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

on 00.2.14 4:03 PM, fiona at reply at newsgroup.please 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
> 
You have to solve the recurrence equation first. You can either do it by
hand, (since the answer is obvious), or use Mathematica:

In[6]:=
<< DiscreteMath`RSolve`

In[7]:=
RSolve[{a[n] == 2*a[n - 1], a[1] == 2}, a[n], n]

Out[7]=
           n
{{a[n] -> 2 }}

Once you know this you can use Solve:

In[8]:=
Solve[Sum[2^i, {i, 1, n}] == 62, n]

Solve::"ifun": "Inverse functions are being used by \!\(Solve\), so some \
solutions may not be found."

Out[8]=
{{n -> 5}}


--
Andrzej Kozlowski
Toyama International University
Toyama, Japan
http://sigma.tuins.ac.jp/




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