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needhelp83
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Derive a simplified formula for the c.d.f., F(n) = (P [tex]\leq [/tex] n), using:
[tex]\sum_{k=0}^{n}r^k=\frac{1-r^{n+1}}{1-r} [/tex]
[tex]p(n)=\alpha (1-\alpha)^n [/tex]
[tex]\alpha \sum_{k=0}^{n}r^k=\frac{1-(1-\alpha)^{n+1}}{1-(1-\alpha)} [/tex]
How do I break this down to a simplified version?
[tex]\sum_{k=0}^{n}r^k=\frac{1-r^{n+1}}{1-r} [/tex]
[tex]p(n)=\alpha (1-\alpha)^n [/tex]
[tex]\alpha \sum_{k=0}^{n}r^k=\frac{1-(1-\alpha)^{n+1}}{1-(1-\alpha)} [/tex]
How do I break this down to a simplified version?
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