[1]Sn=1=+2.5+3.5^2+...+n.5^n+1 [2]Sn=1/2+2/2^2+3/2^3+...+n/2n
问题描述:
[1]Sn=1=+2.5+3.5^2+...+n.5^n+1 [2]Sn=1/2+2/2^2+3/2^3+...+n/2n
答
(1)利用错位相减法:公比q=5Sn=1*5^0+2*5^1+3*5^2+4*5^3+-----+n*5^(n-1)----(1)5*Sn=1*5+2*5^2+3*5^3+4*5^4+-----+n*5^n-----(2)(1)-(2)-4*Sn=1+5+5^2+5^3+----+5^(n-1)-n*5^n=(1-5^n)/(1-5)-n*5^nSn=n*5^n/4+(1-5^...