which of the following is the correct expanded form for the series below? \n∑(n = 1 to 4) n/n! \n1 + 1 + 1/2…

Explanation:

Step1: Recall the sum - notation formula

The sum $\sum_{n = 1}^{4}\frac{n}{n!}$ means we substitute $n=1,2,3,4$ into $\frac{n}{n!}$ and add the results.

Step2: When $n = 1$

Substitute $n = 1$ into $\frac{n}{n!}$, we get $\frac{1}{1!}=\frac{1}{1}=1$.

Step3: When $n = 2$

Substitute $n = 2$ into $\frac{n}{n!}$, we have $\frac{2}{2!}=\frac{2}{2\times1}=1$.

Step4: When $n = 3$

Substitute $n = 3$ into $\frac{n}{n!}$, we obtain $\frac{3}{3!}=\frac{3}{3\times2\times1}=\frac{1}{2}$.

Step5: When $n = 4$

Substitute $n = 4$ into $\frac{n}{n!}$, we get $\frac{4}{4!}=\frac{4}{4\times3\times2\times1}=\frac{1}{6}$.

Step6: Calculate the sum

$\sum_{n = 1}^{4}\frac{n}{n!}=1 + 1+\frac{1}{2}+\frac{1}{6}$.

Answer:

$1 + 1+\frac{1}{2}+\frac{1}{6}$