Question

Sigma Notation Determining sums ????

Answer 1

name one

Answer 2

\[\sum_{k=1}^{\infty} (1/10^{k}\]

Answer 3

\[\sum_{k=1}^{\infty} ( 3/ 10^{k} )\]

Answer 4

ok you actually know what this is without any work. we can do the work, but this is
\[.3333=\overline{.3}\] which your recognize as
\[\frac{1}{3}\]

Answer 5

but how do you do the work?

Answer 6

you can use
\[\sum_{k=1}^\infty ar^k=\frac{a}{1-r}\] in this case
\[a=\frac{3}{10},r=\frac{1}{10}\] so you get
\[\frac{\frac{3}{10}}{1-\frac{1}{10}}=\frac{\frac{3}{10}}{\frac{9}{10}}=\frac{3}{9}=\frac{1}{3}\]

Answer 7

how do you get the r ?