作业帮设等差数列前N项的和为SN,若SN=SM,则S(M+N)=?
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设等差数列前N项的和为SN,若SN=SM,则S(M+N)=?
设等差数列前N项的和为SN,若SN=SM,则S(M+N)=?
设等差数列前N项的和为SN,若SN=SM,则S(M+N)=?
SN=SM
→n(a1)+(d/2)n(n-1)=m(a1)+(d/2)m(m-1)
→(n-m)(a1)+(d/2)[n^2-m^2-(n-m)]=0
→(n-m)(a1)+(d/2)(n-m)(n+m-1)=0
→a1+(d/2)(n+m-1)=0
→2(a1)+(n+m-1)d=0
→a1+[a1+(n+m-1)d]=0
→a1+a(n+m)=0.
∴S(n+m)＝(n+m)[a1+a(n+m)]/2＝0.
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