Question Statement :

Second term of a geometric progression is 1000 and the common ratio is = 1/n, where n is a natural number. $P_n$ is the product of n terms of this GP.$P_{6 }>P_5$ and $P_{6 }>P_7$ ; what is the sum of all possible values of n?

Type in your answer as an integer. For example, if your answer is 9, type 9