高考累乘法n≥2时an an-1=根号下3n-2 3n-5 a1=1
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在原式基础上,再写一相同结构等式,到an+2结束.减去原式便得到:1/(an+1)an=n+1/(an+1)(an+2)-n/anan+1整理得…你题目可能出错了,不是等差数列.我们假设公差为d.那么
n=1,S1=a1=2,n>1,an=Sn-S(n-1)=2n,n=1时也适合,故:an=2nbn=(1/4)·1/n(n+1)4bn=1/n(n+1)=1/n-1/(n+1),所以:4Tn=[(1-
(Ⅰ)∵数列{an}满足a1=1,an+1=2n+1anan+2n(n∈N*),∴2n+1an+1=2nan+1,即2n+1an+1−2nan=1,∴数列{2nan}是公差为1的等差数列.(Ⅱ)由(Ⅰ
an*a(n-1)=a(n-1)+(-1)^nan=1+(-1)^n/a(n-1)a1=1a2=1+1/1=2a3=1-1/2=1/2a4=1+1/1/2=3a5=1-1/3=2/3a5/a3=(2/
设A1A2=a则:由于在数列{An}中An小于0故a>0,且An+1An+2/AnAn+1>0即q>0;由题中:2AnAn+1+An+1An+2>An+2An+3得2aq^(n-1)+aq^n>aq^
an=(n+1)/2bn=4/(n+1)(n+2)=4(1/(n+1)-1/(n+2))bn的前n项和为4*(1/2-1/3+1/3-1/4+……+1/(n+1)-1/(n+2))=4(1/2-1/(
原式=1/(5×7)+1/(7×9)+1/(9×11)+.+1/[(2n+3)(2n+5)]=1/2[(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+.+1/(2n+3)-1/(2n+5
an*a(n+1)=2^na(n-1)*an=2^(n-1)所以:a(n+1)/a(n-1)=2a1=1,所以a2=2(此时分奇数和偶数讨论)a(2n+1)=2^n,a(2n)=2^n所以a9=2^4
an=1/(n+1)+2/(n+1)+...+n/(n+1)=(1+2+...+n)/(n+1)=[n(n+1)/2]/(n+1)=n/2bn=2/[ana(n+1)]=2[(n/2)(n+1)/2]
a1=S1=20-1=19,an=Sn-Sn-1=-2n+21,n≥2a1时也符合∴an=-2n+21anan+1=(-2n+21)(-2n+19)<0∴192<n<212∵n∈N∴n=10故答案为:
Sn=2n^2+nSn-1=2(n-1)^2+n-1an=Sn-Sn-1=4n-1lim[1/a1a2+1/a2a3+1/a3a4+...+1/anan+1]=lim[1/3*1/7+1/7*1/11
n=(-1)^(n-1).4n/[an.a(n+1)]=(-1)^(n-1).4n/[(2n-1)(2n+1)]=(-1)^(n-1).[1/(2n-1)+1/(2n+1)]Tn=b1+b2+b3+.
由(an-1-an)/(anan-1)=(an-an+1)/(anan+1)(n≥2),得到1/an-1/a(n-1)=1/a(n+1)-1/an{1/an}是等差数列,而且公差d=1/a2-1/a1
参考百度,】an=2n,即246810121416a1a2+…+anan+1=An,即8244880120168……An=4n(n+1)平方和的公式为S=n(n+1)(2n+1)/6所以,Sn=4×n
由题意得1/a1a2+1/a2a3…1/anan-1=(n-1)/a1an①原式-①得1/anan+1=n/a1an+1-(n-1)a1an整理得2=nan-(n-1)an+1两边同时除以n(n-1)
an=(1+2+.+n)/nan=[n(1+n)/2]/n=(1+n)/2a1=(1+1)/2=1a(n+1)=(2+n)/21/an=2/(1+n)1/a(n+1)=2/(2+n)bn=1/[ana
由题意:n=1时,a2*a1=a2*1=2,即a2=2n=2时,a2*a3=4,即a3=2当n>=2时,anan+1=2^nan-1an=2^(n-1)故an+1/an-1=2所以隔项成等比数列当n为
(1)∵anan+1=2n,∴anan-1=2n-1,两式相比:an+1an−1=2,∴数列{an}的奇数项成等比数列,偶数项成等比数列,∵a1=1,a nan+1=2n(n∈N*)∴a1=
an=(1+2+.+n)/nan=[n(1+n)/2]/n=(1+n)/2a1=(1+1)/2=1a(n+1)=(2+n)/21/an=2/(1+n)1/a(n+1)=2/(2+n)bn=1/[ana