有一个等比数列的求和公式S=a1(1-q^n)/1-q [其中q不等于1],推导方法按照最佳答案来,_百度知道
有一个等比数列的求和公式S=a1(1-q^n)/1-q [其中q不等于1],推导方法按照最佳答案来,
提问者采纳
设公比为qS=a1+a2+a3+a4+……+an
=a1+a1q+a1q^2+a1q^3+……+a1q^(n-1)
①等式两边同乘以公比q,得(1-q)S=a1-a1q^n【中间项都消掉了】
=a1(1-q^n)S=a1(1-q^n) /,得qS=a1q+a1q^2+a1q^3+a1q^4+……+a1q^(n-1) +a1q^n
② ① - ②【错位相减】证明
提问者评价
谢谢。。。
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....设一等比列B1=a1(a1不为0)
Bn=a1* q^(n-1)
[其中q不等于1]
则Sn=B1+B2+B3+
.....B(n-1)+Bn+B(n+1)下式减上式得(q-1)Sn=B(n+1)-B1
又B(n+1)-B1=a1* q^n -a1
所以得Sn=a1(1-q^n)/..B(n-1)+Bn则等式两边同时乘以q
得qSn=B2+B3+
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