prove the geometric progress: u = sum[n=1, infty] [np(1-p)^{n-1}], u = 1/p

[gunmo]

Hi

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Prove Geometric progress.

. . . . .\(\displaystyle \displaystyle u\, =\, \sum_{n=1}^{\infty}\, np(1\, -\, p)^{n-1}\)

. . . . .\(\displaystyle u\, =\, \dfrac{1}{p}\)

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My Statistic text book does not prove this.
Thank you

Gu.

 

[mmm4444bot]

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[stapel]

Prove the following Geometric progression.

. . . . .\(\displaystyle \displaystyle u\, =\, \sum_{n=1}^{\infty}\, np(1\, -\, p)^{n-1}\)

. . . . .\(\displaystyle u\, =\, \dfrac{1}{p}\)

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My Statistic text book does not prove this.

Okay. What progressions does your book prove? What formulas does it just give you, without proof? Are you supposed to use proof by induction, or some other specified method?

When you reply, please include a clear listing of your thoughts and efforts so far, so we can see where you're getting stuck. Thank you!