Question

why this summation
∑j=1to n+1((n+1)!/(n+1−j)!(j)!)pj(1−p)n+1−j
= (1-(1-p)
n+1
)

Answer 1

\[\sum_{j=0}^{n+1}((n+1)!/(n+1−j)!(j)!)p ^{j} (1−p)^{ n+1−j }\] =(1-(1-p)
\[^{n+1}\]
)

Answer 2

=1/(1-p)^n??????

Answer 3

=1/(1-p)^(n+1) ???????

Answer 4

1-(1-p)^(n+1)