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"Sₙ=1/2n(a₁+aₙ)=(d/2)n²+(a₁-d/2)n
Sₙ=n×a₁(q=1)
Sₙ=a₁×(1-qⁿ)/(1-q)=(a₁-aₙ×q)/(1-q)(q≠1)
Sₙ=n(n+1)/2
Sₘₙ=(n+m)(n-m+1)/2
求和公式的性质:
1、在等差数列中,若Sn为该数列的前n项和,S2n为该数列的前2n项和,S3n为该数列的前3n项和,则Sn,S2n-Sn,S3n-S2n也为等差数列。
2、余下的项具有如下的特点:余下的项前后的位置前后是对称的;余下的项前后的正负性是相反的。
3、有一类数列,既不是等差数列,也不是等比数列,若将这类数列适当拆开,可分为几个等差、等比或常见的数列,然后分别求和,再将其合并即可。"