错位相减发求数列和 an=(3n-1)*2^n

问题描述:

错位相减发求数列和 an=(3n-1)*2^n
错位相减发求数列和 an=(3n-1)乘以2的n次方 速求

an=(3n-1)*2^nSn=2*2^1+5*2^2+8*2^3+…+(3n-4)*2^(n-1)+(3n-1)*2^n那么2Sn=2*2^2+5*2^3+8*2^4+…+(3n-4)*2^n+(3n-1)*2^(n+1)两式相减,得:-Sn=2*2^1+3*2^2+3*2^3+…+3*2^(n-1)+3*2^n-(3n-1)*2^(n+1)=4+3*[2^2...