So, how do I solve this to find the value of n ?
Un = (-1)^n (n / n + 4) and I know that Un = 7 / 9 ?
So do you times (-1)^n and ( n / n + 4) ??
Someone help me out here, with explanation please!
Are you asking for which $\displaystyle n$ value $\displaystyle u_{n}=\frac{7}{9}$ holds?
If so, $\displaystyle n=14$.
To find the solution, first consider $\displaystyle n=2k$ then $\displaystyle n=2k-1$ for $\displaystyle k\in\mathbb{N}$.
In the first case, you will find $\displaystyle k=7$ ($\displaystyle n=14$) and in the second one $\displaystyle k=-\frac{3}{8}\not\in\mathbb{N}$.
you are somewhat vague, Mathematix, but if bkarpuz's last post accurately said what you want, then you must solve $\displaystyle \frac n{n + 4} = \frac 79$ for $\displaystyle n$. and note that $\displaystyle n$ must be even. so if you get an odd number, you are wrong