Re: solving an equation with sums

• To: mathgroup at smc.vnet.net
• Subject: [mg67483] Re: [mg67469] solving an equation with sums
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Wed, 28 Jun 2006 03:51:24 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```expr = (2*(1 - E^((-x)*0.1) - 2810)*0.1)/E^(x*0.1) +
(2*(1 - E^((-x)*0.2) - 5411)*0.2)/E^(x*0.2) +
(2*(1 - E^((-x)*0.3) - 8701)*0.3)/E^(x*0.3) +
(2*(1 - E^((-x)*0.4) - 13130)*0.4)/E^(x*0.4) +
(2*(1 - E^((-x)*0.5) - 17327)*0.5)/E^(x*0.5) +
(2*(1 - E^((-x)*0.6) - 24899)*0.6)/E^(x*0.6) +
(2*(1 - E^((-x)*0.7) - 31230)*0.7)/E^(x*0.7) +
(2*(1 - E^((-x)*0.8) - 40006)*0.8)/E^(x*0.8) +
(2*(1 - E^((-x)*0.9) - 59880)*0.9)/E^(x*0.9) +
(2*(1 - E^(-x) - 80017))/E^x;

where I have corrected what appear to be typos (i.e., t[[i]] had different values in terms of the expression)

If you Plot the LHS of the equation it approaches zero from below but never gets there. Let's use -1 instead of zero. However, "Solve deals primarily with linear and polynomial equations" (from the Help browser); you should use FindRoot.

FindRoot[expr == -1, {x, 1}]

{x -> 63.3796}

Note that the expression can be written directly with the lists

t=Table[t,{t,.1,1,.1}];

f={2810,5411,8701,13130,17327,24899,31230,40006,59880,80017};

expr==Total[2*(1-E^(-x*t)-f)*t*E^(-x*t)]

True

Bob Hanlon

---- "newbix at bk.ru" <newbix at bk.ru> wrote:
> Hello,
>
> I try to solve the following equation:
> sum[2*(1-e^(-x*t[[i]])-F[[i]])*t[[i]]*e^(-x*t[[i]]),{i,1,10}]==0
> where t and F are lists. Each list has ten entries.
> I tried to solve this sum using the following command:
> ------------------------------------------------------
> Solve[2*(1 - \[ExponentialE]^(-x*0.1) - 2810)*0.1*\[ExponentialE]^(-x*0.1) +
>       2*(1 - \[ExponentialE]^(-x*0.2) - 5411)*0.2*\[ExponentialE]^(-x*0.2) +
>       2*(1 - \[ExponentialE]^(-x*0.3) - 8701)*0.3*\[ExponentialE]^(-x*0.3) +
>       2*(1 - \[ExponentialE]^(-x*0.4) - 13130)*0.4*\[ExponentialE]^(-x*0.4) +
>       2*(1 - \[ExponentialE]^(-x*0.5) - 17327)*0.5*\[ExponentialE]^(-x*0.5) +
>       2*(1 - \[ExponentialE]^(-x*0.6) - 24899)*0.6*\[ExponentialE]^(-x*0.6) +
>       2*(1 - \[ExponentialE]^(-x*0.7) - 31230)*0.7*\[ExponentialE]^(-x*0.7) +
>       2*(1 - \[ExponentialE]^(-x*0.7) - 40006)*0.8*\[ExponentialE]^(-x*0.8) +
>       2*(1 - \[ExponentialE]^(-x*0.8) - 59880)*0.9*\[ExponentialE]^(-x*0.9) +
>       2*(1 - \[ExponentialE]^(-x) - 80017)*\[ExponentialE]^(-x) == 0, x]
> -----------------------------------------
> but I got the following error message:
>
> Solve::"tdep": "The equations appear to involve the variables to be solved \
> for in an essentially non-algebraic way."
>
> What's wrong? How can I solve this expression using Mathematica?
>