作业帮设Sn是等差数列｛an｝的前n项和,求证：若正整数m,n,p成等差数列,则Sm/m,Sn/n,Sp/p也成等差数列.
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设Sn是等差数列｛an｝的前n项和,求证：若正整数m,n,p成等差数列,则Sm/m,Sn/n,Sp/p也成等差数列.
设Sn是等差数列｛an｝的前n项和,求证：若正整数m,n,p成等差数列,则Sm/m,Sn/n,Sp/p也成等差数列.
设Sn是等差数列｛an｝的前n项和,求证：若正整数m,n,p成等差数列,则Sm/m,Sn/n,Sp/p也成等差数列.
Sn=[(a1+a1+(n-1)d]*n/2=[2a1+(n-1)d)]*n/2
Sm/m={[2a1+(m-1)d)]*m/2}/m=a1+(m-1)d/2
Sn/n=a1+(n-1)d/2
Sp/p=a1+(p-1)d/2
2Sn/n=2a1+(n-1)d
m,n,p成等差数列,2n=m+p
(Sm/m)+(Sp/p)
=a1+(m-1)d/2+a1+(p-1)d/2
=2a1+(m+p-2)d/2
=2a1+(2n-2)d/2
=2a1+(n-1)d
2Sn/n=(Sm/m)+(Sp/p)
Sm/m,Sn/n,Sp/p也成等差数列
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