Question

5.已知数列{an}中有相邻两项a2k-1,a2k是关于x的方程的两个根,且a2k-1a2k(k=1,2,3,…)

Answer 1

Bn=3 (n=1)

Bn=n*2n (n>=2)

Sn=B1+B2+B3+.+Bn

=3+2*22+3*23+……+n*2n (1)

2Sn=6+2*23+3*24+.+（n-1)*2n+n*2n+1 (2)

(2)-(1):

Sn=3-(23+24+25….+2n-1)-2*22+n*2n+1

=3-(2n-23)-8+n*2n+1

=n*2n+1-2n+3