Question

已知数列{an}满足（1/1-an+1）-（1/1-an）=1,且a1=0

Answer 1

(1)

（1/(1-a(n+1))）-（1/(1-an)）=1

=>{1/(1-an)}是等差数列,d=1

1/(1-an)-1/(1-a1)=n-1

1/(1-an) = n

1-an =1/n

an = (n-1)/n

(2)

bn=n.an

=n-1

Sn =b1+b2+...+bn

= (n-1)n/2

(3)

cn=(1-√a(n+1)）/√n

=( 1- √[n/(n+1)] )/√n

= (√(n+1) - √n ) /(√(n+1).√n)

= 1/√n - 1/√(n+1)

Tn = c1+c2+...+cn

= 1 - 1/√(n+1)