求数列3/2,9/4,25/8,65/16,161/32的sn

求数列3/2,9/4,25/8,65/16,161/32的sn
求数列3/2,9/4,25/8,65/16,161/32的sn

求数列3/2,9/4,25/8,65/16,161/32的sn
an=n+1/2^n
Sn=(1+2+……+n)+(1/2+1/4+……+1/2^n)
=(1+n)n/2+1/2(1-1/2^n)/(1-1/2)
=n²/2+n/2+1-1/2^n