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**Type : **Subjective

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*