等差数列｛an｝的前n项和为Sn,且满足Sp=Sq（p,q属于正整数,p≠q）,则Sp+q=?

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等差数列｛an｝的前n项和为Sn,且满足Sp=Sq（p,q属于正整数,p≠q）,则Sp+q=?
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等差数列｛an｝的前n项和为Sn,且满足Sp=Sq（p,q属于正整数,p≠q）,则Sp+q=?
等差数列｛an｝的前n项和为Sn,且满足Sp=Sq（p,q属于正整数,p≠q）,则Sp+q=?

等差数列｛an｝的前n项和为Sn,且满足Sp=Sq（p,q属于正整数,p≠q）,则Sp+q=?
Sn=(a1+an)n/2=na1+n(n-1)d/2
Sp=pa1+p(p-1)d/2
Sq=qa1+q(q-1)d/2
Sp=Sq
2(p-q)a1=[q(q-1)-p(p-1)]d=(q-p)(q+p-1)d
a1=-(q+p-1)d/2
S(p+q)=(p+q)a1+(p+q)(p+q-1)d/2
=-(p+q)(q+p-1)d/2+(p+q)(p+q-1)d/2
=0

等于0，自己算算吧

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