设数列{a}满足an+1=an+1/n(n+1）a20=1则a1=?如题

Question

设数列{a}满足an+1=an+1/n(n+1） a20=1 则a1=?
如题

Answer 1

a(n+1)=an+1/[n(n+1）]
a(n+1)-an = 1/[n(n+1)]
= 1/n - 1/(n+1)
an - a(n-1) = 1/(n-1) - 1/n
an - a20 = 1/20 - 1/n
an = (21/20) -1/n
n=1
a1 = (21/20) -1
= 1/20