a4= a2+ 1+2

a6= a2+ 1+2+2+3

…

a2n = a2+ 1+2[2+3+4+…+(n- 1)]+n

= a2+n+ 1+2 *(2+n- 1)(n-2)/2

= a2+n+ 1+( 1+n)(n-2)

= a2+n2- 1

Because a2= a 1+ 1, a 1=0.

So: a2n= n2- 1+ 1= n2.

bn =(2n+ 1)2/a2n+ 1 =(2n+ 1)2/(a2n+n)=(2n+ 1)2/(N2+n)= 4+ 1/(N2+n)

sn = b 1+B2+…+bn = 4n+( 1- 1/2+ 1/2- 1/3+…+ 1/n- 1/(n+ 1))

=4n+n/(n+ 1)