已知an=2n(n∈N*),则a1a2+a2a3+a3a4+……+anan+1=
问题描述:
已知an=2n(n∈N*),则a1a2+a2a3+a3a4+……+anan+1=
答
参考百度,】an=2n,即2 4 6 8 10 12 14 16 a1a2+…+anan+1=An,即8 24 48 80 120 168 ……An=4n(n+1)平方和的公式为S=n(n+1)(2n+1)/6所以,Sn=4×n(n+1)(2n+1)/6+4×n(n+1)/2=2n(n+1)(2n+1)/3+2n(n+1)=2n(n+1)(2n...