求和1+2的平方分之3+2的立方方分之4+2的四次幂分之5+···+2的(n-1)次幂分之n+2

错位相减法Sn=2/2^1+3/2^2+4/2^3+5/2^4 +.+n+2/2^n-1两边同时乘以22Sn=2+3/2^1+4/2^2+5/2^3+.+(n+2)/2^n-2相减得Sn=2-(n+2)/2^n-1 +(1/2^1 +1/2^2 +.+1/2^n-2)=2-(n+2)/2^n-1+(1-1/2^n-2)=3- (4n+9)/2^n-2...