Expand the partial sum and find its value type your answer as an improper fraction:sigma (sum) starting value (k) at 0 ending value 3, function is 4/k!The sum is Answer

Question

asked Jan 10, 2023 66.0k views

1 Answer

Allysha · Answer 1 · 2023-01-15T11:43:08+0000

Solution:

Given:

$\sum_{k\mathop{=}0}^3(4)/(k!)$

This implies that the value of k starts from 0 and ends at 3.

Thus, the partial sum is expanded to be

Where

$\begin{gathered} (4)/(0!)=(4)/(1)=4 \\ (4)/(1!)=(4)/(1)=4 \\ (4)/(2!)=(4)/(2)=2 \\ (4)/(3!)=(4)/(6)=(2)/(3) \end{gathered}$

Thus, we have

$\begin{gathered} 4+4+2+(2)/(3) \\ =(32)/(3) \end{gathered}$

Hence, the sum is