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+(1)/(2) +(1)/(6)`

Step-by-step explanation:

we will substitute the values of n in given expression

`\sum_(n=1)^(4)(n)/(n!)`

when substituting n=1 we get in
`\sum_(n=1)^(4)(n)/(n!)`=
`(1)/(1!)`

when n=2 we get
`(2)/(2!)`

when n =3 we get
`(3)/(3!)=(3)/(6)=(1)/(2)` ;3 factorial that is 3! = 3 *2*1 = 6

when n=4 we get
`(4)/(4!)=(4)/(24)=(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