Question 935306
<pre>
{{{U[n]=(n/(n+4))(-1)^n}}} where {{{U[n]= 7/9}}}

{{{7/9=(n/(n+4))(-1)^n}}}

{{{7(n+4)=9n(-1)^n}}}

{{{7n+28=9n(-1)^n}}}

if n is odd, {{{(-1)^n=-1}}}

{{{7n+28=9n(-1)}}}

{{{7n+28=-9n}}}

{{{28=-16n}}}

{{{28=-16n}}}

{{{n=28/(-16)}}}, 

{{{n=-7/4}}}, not a non-negative integer, 
so there is no solution for n being odd.

so n must be even, {{{(-1)^n=1}}}

{{{7n+28=9n(1)}}}

{{{7n+28=9n}}}

{{{-2n=-28}}}

{{{n=28/2}}}

{{{n=14}}}

Checking:

{{{U[n]=(n/(n+4))(-1)^n}}}

{{{U[14]=(14/(14+4))(-1)^14}}}

{{{U[14]=(14/18)(1)}}}

{{{U[14]=7/9}}}

That checks:

Answer: {{{n=14}}}

Edwin</pre>