solving an equation with sums

• To: mathgroup at smc.vnet.net
• Subject: [mg67469] solving an equation with sums
• From: "newbix at bk.ru" <newbix at bk.ru>
• Date: Tue, 27 Jun 2006 03:14:39 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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?