Question

4Σn=! n/n!

I understand what the denominator, n! is by definition. I just don't understand what to put for the numerator when n = !

Can anyone help me figure this out?

Answer 1

I think the sum is supposed to be

`\displaystyle\sum_(n=1)^4\frac n{n!}=\sum_(n=1)^4\frac1{(n-1)!}`

since
`n!=n\cdot(n-1)!`. Then

`\displaystyle\sum_(n=1)^4\frac1{(n-1)!}=\frac1{0!}+\frac1{1!}+\frac1{2!}+\frac1{3!}`

and
`0!=1` by definition so that the sum has a value of
`\frac83`.