Question

what is s_10 for 1+3+9+27 + ....?

Answer 1

hint:
here we have a geometri series, whose constant \(r\) is:
\[\Large r = \frac{{27}}{9} = \frac{9}{3} = \frac{3}{1} = 3\]

Answer 2

geometric*

Answer 3

now, the requested sum \(S_{10}\), is:
\[\Large {S_{10}} = {a_1} \cdot \frac{{{3^{10}} - 1}}{{3 - 1}}\]
where \(a_1=1\) is the first term of the series

Answer 4

then we can write:
\[\Large {S_{10}} = {a_1} \cdot \frac{{{3^{10}} - 1}}{{3 - 1}} = 1 \cdot \frac{{{3^{10}} - 1}}{{3 - 1}} = ...?\]

Answer 5

29,524 ?

Answer 6

Thank you

Answer 7

that's right! :)