Because a10 * a24 = a 172 (a172 stands for the square of a17).

So a 10= 1.

Then a1= a10/(q 9) =1/q 9; a2= 1/q^8； a3= 1/q^7； ……

a 10= 1，a 1 1 = a 10 * q = q； a 12=q^2； a 13=q^3； ……; a 19=q^9； ……

So the left inequality A1+A2+A3+...+An =1/Q 9+1/Q 8+1/Q 7+...+1+Q 2+.

On the right of the inequality is1/a1+1/a2+1a3+...+1/an = q 9+q 8+q 7+...+1+.

Compared with ① ②, when n= 19, ① = ②.

When q> 1, make ① >; ②, it must be n> 19.

When 0; ②, which must be 0.