早教吧作业答案频道 -->数学-->
已知S(1)、S(2),证(r+1)S(2)=(r-1)S(1)^2+2aS(1).S(1)=a+ar+ar^2+.+ar^(n-1)S(2)=a^2+a^2r^2+a^2r^4+.+a^2r^2(n-1)证(r+1)S(2)=(r-1)S(1)^2+2aS(1).
题目详情
已知S(1)、S(2),证(r+1)S(2) = (r-1)S(1)^2 + 2aS(1).
S(1) = a + ar +ar^2 + .+ ar^(n-1)
S(2) = a^2 + a^2 r^2 + a^2 r^4 +.+ a^2 r^2(n-1)
证(r+1)S(2) = (r-1)S(1)^2 + 2aS(1).
S(1) = a + ar +ar^2 + .+ ar^(n-1)
S(2) = a^2 + a^2 r^2 + a^2 r^4 +.+ a^2 r^2(n-1)
证(r+1)S(2) = (r-1)S(1)^2 + 2aS(1).
▼优质解答
答案和解析
两个都是等比数列,用等比公式求和.
S(1) = a*(r^n - 1) / (r-1)
S(2) = a^2 * (r^2n - 1) / (r^2 - 1)
则 (r-1)S(1)^2 + 2aS(1) = a^2 * (r^n - 1)^2 / (r-1) + 2a^2 * (r^n -1) / (r-1)
= a^2 *[ (r^n - 1)^2 + 2 (r^n -1) ] / (r-1)
= a^2 *[ r^2n -1 ] / (r-1)
(r+1)S(2) = (r+1) a^2 * (r^2n - 1) / (r^2 - 1) = a^2 *[ r^2n -1 ] / (r-1)
所以(r+1)S(2) = (r-1)S(1)^2 + 2aS(1)成立
S(1) = a*(r^n - 1) / (r-1)
S(2) = a^2 * (r^2n - 1) / (r^2 - 1)
则 (r-1)S(1)^2 + 2aS(1) = a^2 * (r^n - 1)^2 / (r-1) + 2a^2 * (r^n -1) / (r-1)
= a^2 *[ (r^n - 1)^2 + 2 (r^n -1) ] / (r-1)
= a^2 *[ r^2n -1 ] / (r-1)
(r+1)S(2) = (r+1) a^2 * (r^2n - 1) / (r^2 - 1) = a^2 *[ r^2n -1 ] / (r-1)
所以(r+1)S(2) = (r-1)S(1)^2 + 2aS(1)成立
看了 已知S(1)、S(2),证(...的网友还看了以下:
已知向量a=(2,1),b=(x,y).(1)若x∈{-1,0,1,2},y∈{-1,0,1},求向 2020-03-30 …
几道数学计算题(请写过程)第一题1/2+(1/3+2/3)+(1/4+2/4+3/4)+…+(1/ 2020-05-16 …
2^2-1^2=2*1+13^2-2^2=2*2+14^2-3^2=2*3+1……(n+1)^2- 2020-05-19 …
已知S=1+(-1/2)+1/2+(-1/3+1/3+(-1/4)+.+1/2014+(-1/20 2020-06-11 …
设向量组(Ⅰ)α1,α2,…αs的秩为r1,向量组(Ⅱ)β1,β2,…βs的秩为r2,且向量组(Ⅰ 2020-06-30 …
线性代数1.设α1,α2,…,αs的秩为r且其中每个向量都可以由α1,α2,…αr线性表示,证明: 2020-06-30 …
求1+2+2^2+2^3+2^4+…+2^2014的值.设S=1+2+2^2+2^3+2^4+…+ 2020-07-09 …
(2000•内江)(1)观察下列等式:1(1+1×2)(1+2×2)=12(11+1×2−11+2× 2020-11-12 …
观察下列等式:1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4.在线等 2020-12-05 …
证明:1/(x+1)+1(x+2)…+1/(3n+1)>=1证明:当n=1时,1/2+1/3+1/4 2020-12-23 …