Question

does the sum from n=0 to infinity of (7^n)/(9^(n+1)) converge or diverge

Answer 1

it converges

Answer 2

what did u do to sole that
like what test

Answer 3

i can tell it converges but by what test? integral seems as though it would be too complicated

Answer 4

vn=1/3^(2n+2) it will produce a finite value

Answer 5

can you explain that please

Answer 6

\[7^n/(9^(n+1)=\]
\[7^n/(9^n).9=\]
\[(1/9).(7/9)^n\]

IOW the individual terms tend to zero meaning it could converge.

next step integrate the series as if it were a function and if the sum < infinity, it does converge.

Integrate {(1/)(7/9)^n} dn and you should get (1/9)(1/n)((7/9)^(n=1)), 7^2/ 9^3

or note that the ratio between successive terms is < 1 so it converges under the Ratio test...

make sense....?