write-the-following-recursive-function-in-explicit-form-f-1-1-f-n-1-n-1-f-n-n-

Question Number 205919 by Red1ight last updated on 03/Apr/24

write the following recursive function in explicit form

f (1) = 1

f (n + 1) = (n + 1) f (n) + n!

Answered by Tinku Tara last updated on 03/Apr/24

f (n) = (n) f (n - 1) + (n - 1)!

f (n) = n f (n - 1) + \frac{n!}{n}

= n [(n - 1) f (n - 2) + \frac{(n - 1)!}{(n - 1)}] + \frac{n!}{n}

= n (n - 1) f (n - 2) + \frac{n!}{(n - 1)} + \frac{n!}{n}

continue

f (n) = n! + \underset{i = 2}{\sum^{n}} \frac{n!}{i}