Question

Help please!! It's an infinite serie
\[\displaystyle\sum_{n=1}^\infty \dfrac{n}{3^n}\]

Answer 1

\[\displaystyle\sum_{n=1}^\infty \dfrac{n}{3^n}
\]

Answer 2

please i need the solution

Answer 3

i think it is the derivative of a geometric series

Answer 4

without the \(n\) up top it would be \(\frac{1}{1-\frac{1}{3}}\) but with the \(n\) it is
\[\frac{1}{(1-\frac{1}{3})^2}\]

Answer 5

oh and if you are starting at \(n=1\) instead of \(n=0\) you have to subract \(1\)

Answer 6

that is not right what i just said
since you are starting at \(n=1\) it is
\[\frac{\frac{1}{3}}{(1-\frac{1}{3})^2}\]