Practice By Tag: Newton's Binomial Theorem

Question: 2013 Fall Midterm - 9

1 . Which of the following is true?

(a)

$\sum_{k=0}^{n} 5^{k}{{n}\choose{k}} = 5^{n}$

(b)

$\sum_{k=0}^{n} 4^{k}5^{n-k}{{n}\choose{k}} = 20^{n}$

(c)

$\sum_{k=0}^{n} 5^{k}{{n}\choose{k}} = 6^{n}$

(d)

$\sum_{k=0}^{n} 4^{n-k}5^{k}{{n}\choose{k}} = 8^{n}$