Problem 6

In a sports contest,

m

medals were awarded on

n

successive days (

n>1

). On the first day, one medal and

\frac17

of the remaining

m-1

medals were awarded. On the second day, two medals and

\frac17

of the then remaining medals were awarded, and so on. On the

n

-th and last day, the remaining

n

medals were awarded. Find

m

and

n

Step 4 of 6: Evaluate the geometric sum

m=36+\frac{(n-6)7^n}{6^{n-1}}

Detailed analysis

The standard finite arithmetic-geometric sum simplifies the formula to $m=36+\frac{(n-6)7^n}{6^{n-1}}$ .