$\sum_{j=k-1}^{n-1} \binom{n-1}{j} p^j (1-p)^{n-1-j}$

$\sum_{j=k}^{n-1} \binom{n-1}{j} p^j (1-p)^{n-1-j}$

$\sum_{j=k}^{n} \binom{n}{j} p^j (1-p)^{n-j}$

$p \sum_{j=k-1}^{n-1} \binom{n-1}{j} p^j (1-p)^{n-1-j}$