Show that yn $<1$ for all n and yn decreases monotonically to $0$ as n $->$infty $.($A picture would suffice for this!$)$

$($b$)$ Program the algorithm in a computer and find yn for n $=1,2,...,30.$ What happens? Why does this happen?

$($c$)$ Derive an algorithm for computing the values of these integrals based on evaluating the value of yn$-1$ from the value of yn$.$