高中数列加试题求所有正整数A1,A2...An,使得(99/100)=(A0/A1)+(A1/A2)+...+(An-1

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高中数列加试题
求所有正整数A1,A2...An,使得(99/100)=(A0/A1)+(A1/A2)+...+(An-1/An),其中A0=1,[A(k+1)-1]*A(k-1)>=A(k)*A(k)*[A(k)-1],k=1,2,...n

[A(k+1)-1]*A(k-1)>=A(k)*A(k)*[A(k)-1] (a2-1)*a0=a1^2(a1-1) a0/a1=a1(a1-1)/(a2-1)=a1a2(a1-1)/a2(a2-1)=(a1/a2)*[a2(a1-1)/(a2-1)] a1/a2=(a0/a1)*(a2-1)/a2(a1-1) a2/a3=(a1/a2)*(a3-1)/a3(a2-1)=(a0/a1)*(a3-1)/a2a3(a1-1) a3/a4=(a2/a3)*(a4-1)/a4(a3-1)=(a0/a1)*(a4-1)/a2a3a4(a1-1) ...a(n-1)/an=[a(n-2)/a(n-1)]*(an-1)/an[a(n-1)-1] =(a0/a1)*(an-1)/a2a3...an(a1-1) 1/a2a3...an=[a(n-1)/an]*(a1/a0)*(a1-1)/(an-1) a0/a1+a1/a2+...+a(n-1)/an =(a0/a1)/(a1-1)[a1-1+(a2-1)/a2+(a3-1)/a2a3+...+(an-1)/a2a3...an] =a0/[a1(a1-1)]*[a1-1+1-1/a2+1/a2-1/a2a3+1/a2a3-1/a2a3a4+...+1/a1a2...a(n-1)-1/a2a3...an] =a0/[a1(a1-1)]*[a1-1/a2a3...an] =[1/(a1-1)][(a1a2...an-1)/(a1a2...an)] =99/100 令a1a2...an=A (a1-1)*[A/(A-1)]=100/99 a1=100(A-1)/99A+1=(199A-100)/99A,为正整数,设为N (199A-100)/99A=N A=100/(199-99N) N只能为1,2,N=1时,A=1 又a0=1,因此a1=a2=...an=1,代入,不符合题意.N=2时,A=100 a1=2 可以解得a2=5,a3=51 a1a2a3=510>100,不符合题意,无解.

高中数列加试题求所有正整数A1,A2...An,使得(99/100)=(A0/A1)+(A1/A2)+...+(An-1 求数列a0,a1,a2,a3……a20.已知 a0=0,a1=1,a2=1 a3=a0+2a1+a2 已知数列{an}满足a1+a2+a3+...+an=n^2+2n.(1)求a1,a2,a3,a4 已知数列a0,a1,a2,...,an,...,满足关系式(3-a(n+1))(6+an)=18,且a0=3,则1/a1 一直数列{An}满足A1=1/2,A1+A2+…+An=n^2An 数列an中,已知对任意正整数n,a1+a2+a3+...+an=2^n-1,则a1^2+a2^2+a3^2+...+an 在数列{an}中,已知对任意正整数n,有a1+a2+...+an=(2^n)-1那么a1^2+a2^2+..,+an^2 已知数列{an}满足：a0=1,an=a0+a1+a2+……an-1(n大于等于1),则an = _____ 已知数列{an}满足a0=1,an=a0+a1+a2+...+a(n-1)(n>=1),则当n>=1时,an=? 在数列{an}中,已知对任意正整数n,有a1+a2+...+an=2的n次方-1,那么a1的平方+a2的平方+...+a 数列{an}满足a1=3/2,an+1=an^2-an+1(n属于正整数),则m=1/a1+1/a2+……+1/a200 斐波纳契递推数列：a1=1,an=2(a1+a2+...+an-1) ,求通项公式.