sn等于2分之1+4分之2+8分之3+16分之4+.+n分之2n
Sn=1/2+2/2^2+3/2^3+……+n/2^n
1/2Sn=1/2^2+2/2^3+3/2^4+……+(n-1)/2^n+n/2^(n+1)
二式相减得:
1/2Sn=1/2+1/2^2+1/2^3+……+1/2^n-n/2^(n+1)
1/2Sn=(1/2-1/2^(n+1))/(1-1/2)-n/2^(n+1)
1/2Sn=1-1/2^n-n/2^(n+1)
Sn=2-1/2^(n-1)-n/2^n
因此Sn
sn等于2分之1+4分之2+8分之3+16分之4+.......+2n分之nSn=1/2+2/2^2+3/2^3+……+n/2^n(1)1/2=2分之1,2/2^2=2/4=4分之2,n/2^n=n/(2的n次方)=2n分之n,2n表示n个2相乘,(1)式乘以1/2得:1/2Sn=1/2^2+2/2^3+3/2^4+……+(n-1)/2^n+n/2^(n+1)(2)(1)-(2)式得:1/2Sn=1/2+1/2^2+1/2^3+……+1/2^n-n/2^(n+1)1/2Sn=[1/2+1/2^2+1/2^3+……+1/2^n]-n/2^(n+1)1/2Sn=(1/2-1/2^(n+1))/(1-1/2)-n/2^(n+1)1/2Sn=1-1/2^n-n/2^(n+1)Sn=2-1/2^(n-1)-n/2^n因此Sn
。。。我还以为你是高中生呢你这个题得用到高中的知识小学是做不错来的