# Solve equation which involves sum, binomial coefficient and erf

I want to solve the following equation. Unfortunately solve doesn't do the job. Is there any other way or am I doing something wrong?

Solve[Sum[Binomial[8, d]*1/2*(1 + Erf[(-d + 0.5*(l + k))/(0.215*(l - k)*Sqrt[2])])
, {d, 0, 8}] == n, {k, l, n}]


$k, l, n$ are real numbers.

$n$ should be positive and

$k$ should be smaller than $l$.

I am relatively new to Mathematica and I am sorry if this problem is to trivial for you.

• How would you expect to solve a function with errorfunctions in it analytically? Commented Oct 29, 2016 at 11:37
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– user9660
Commented Oct 29, 2016 at 12:08
• I don't need an analytically correct answer. An approximation would be sufficient. But also NSolve and Reduce won't work Commented Oct 29, 2016 at 13:03
• Well, There's only one equation and 3 unknown, so NSolve[] doesn't have enough to work on. Commented Oct 29, 2016 at 13:08
• But it also doesn't work if I specify two variables... Commented Oct 29, 2016 at 13:15

FindInstance[Sum[Binomial[8, d]*1/2*(1 + Erf[(-d + 0.5*(l + k))/(0.215*(l - k)*Sqrt[2])]),{d, 0, 8}] == n && k < l && n > 0, {k, l, n}, Reals]