Question

Which of the following is the correct expanded form for the series below?

A. 1+1+1/2+1/6
B.1+1/2+1/6+1/24
C.1+2/3+1/2+2/5
D.4+2+2/3+1/6

Answer 1

Answer: Option A is correct  that is $1 +1+\frac{1}{2} +\frac{1}{6}$

Explanation:

we will substitute the values of n in given expression

$\sum_{n=1}^{4}\frac{n}{n!}$

when substituting n=1 we get  in $\sum_{n=1}^{4}\frac{n}{n!}$=$\frac{1}{1!}$

when n=2  we get $\frac{2}{2!}$

when n =3 we get $\frac{3}{3!}=\frac{3}{6}=\frac{1}{2}$ ;3 factorial that is 3! = 3 *2*1 = 6

when n=4 we get  $\frac{4}{4!}=\frac{4}{24}=\frac{1}{6}$;4! = 4*3*2*1 = 24

Note: factorial means the product of the terms getting multiplied  till 1

suppose n! will be equal to n(n-1)(n-2)(n-3).......1