求數列2又1/4,4又1/8,6又1/16,…,2n+1/2^(n+1),…的前n項的和Sn

求數列2又1/4,4又1/8,6又1/16,…,2n+1/2^(n+1),…的前n項的和Sn

2又1/4+4又1/8+6又1/16+,…,+2n+1/2^(n+1)
=(2+4+6+……+2n)+[1/4+1/8+1/16+……+1/2^(n+1)]
=(2+2n)n/2+1/2-1/2^(n+1)
=n(n+1)+1/2-1/2^(n+1)