Question 1071260
<pre>
The terms in x<sup>3</sup> and k<sup>2</sup>  in 
the expansion of (1+kx)<sup>n</sup>  are respectively

{{{(matrix(2,1,n,n-3))k^3x^3}}} and {{{(matrix(2,1,n,n-2))k^2x^2}}}

The coefficients are

{{{(matrix(2,1,n,n-3))k^3}}} and {{{(matrix(2,1,n,n-2))k^2}}}

Since they are equal,

{{{(matrix(2,1,n,n-3))k^3}}}{{{""=""}}}{{{(matrix(2,1,n,n-2))k^2}}}

{{{(matrix(2,1,n,n-3))k}}}{{{""=""}}}{{{(matrix(2,1,n,n-2))}}}

{{{(matrix(2,1,n,3))k}}}{{{""=""}}}{{{(matrix(2,1,n,2))}}}

{{{((n(n-1)(n-2))/3!)k}}}{{{""=""}}}{{{n(n-1)/2!}}}

{{{((n-2))/3!)k}}}{{{""=""}}}{{{1/2!}}}

{{{((n-2))/6)k}}}{{{""=""}}}{{{1/2}}}

{{{(n-2)k}}}{{{""=""}}}{{{3}}}

{{{k}}}{{{""=""}}}{{{3/(n-2)}}}

Edwin</pre>