2^3+2^4+2^5+.+2^(n+1) 的和
问题描述：
2^3+2^4+2^5+.+2^(n+1) 的和
答
令T=2^3+2^4+2^5+.+2^(n+1) 则2T=2^4+2^5+2^6+……+2^(n+2)则T=2T-T=[2^4+2^5+2^6+……+2^(n+2)]-[2^3+2^4+2^5+.+2^(n+1)]=2^(n+2)-2^3=2^(n+2)-8即：2^3+2^4+2^5+.+2^(n+1)=2^(n+2)-82^(n+1)-2^(n+2)*(n+1)这个怎么化简啊2^(n+1)-2^(n+2)*(n+1)
=2^(n+1)-2^(n+1)*2(n+1)
=2^(n+1)*[1-2(n+1)]
=2^(n+1)*(-2n-1)
=-2^(n+1)*(2n+1)