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项数有2n项的等差数列{an},S偶-S奇=?,S偶/S奇=?
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项数有2n项的等差数列{an},S偶-S奇=?,S偶/S奇=?
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解: 项数为2n项的等差数列的奇偶为2你2n/2=n,
S偶=na2+[n(n-1)/2]*d.
=n(a1+d)+n(n-1)d/2.
=na1+nd+n(n-1)d/2.
S奇=na1+n(n-1)d/2.
S偶-S奇=na1+nd+n(n-1)d/2-[na1+n(n-1)d/2].
∴S偶-S奇=nd.
S偶/S奇=[na1+nd+n(n-1)d/2]/[na1+n(n-1)d/2].
=1+nd/[na1+n(n-1)d/2]
S偶=na2+[n(n-1)/2]*d.
=n(a1+d)+n(n-1)d/2.
=na1+nd+n(n-1)d/2.
S奇=na1+n(n-1)d/2.
S偶-S奇=na1+nd+n(n-1)d/2-[na1+n(n-1)d/2].
∴S偶-S奇=nd.
S偶/S奇=[na1+nd+n(n-1)d/2]/[na1+n(n-1)d/2].
=1+nd/[na1+n(n-1)d/2]
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