The question is to find a general formula for the nth term, $a_n$, of the sequence: ${-\frac{2\ln3}{3} , \frac{4\ln4}{9} ,\frac{6\ln5}{27}, \frac{8\ln6}{81} ,\frac{10\ln7}{243},...}$
Here is what I got, but when I plugged in a few terms, it did not work out right. I got the formula to be: $a_n = (-1)^n \frac{2\ln(2+1)\cdot 2^{(n-1)}} {3^n}$
Please help. Thanks