求數列的前n項和 an=1 N(N 2)
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Sn+1/(2n+1)-Sn/(2n-1)=1Sn/(2n-1)=S1+n-1→Sn=(S1+n-1)(2n-1)→Sn=n(2n-1)an=4n-31/√an=2/2√(4n-3)>2/(√4n-3
M=1+2+3+…+n=[n(n+1)]/2N=1²+2²+3²+…+n²=[n(n+1)(2n+1)]/6P=1³+2³+3³+
an=Sn-S(n-1)=n^2-1-[(n-1)^2-1]=2n-1
An=[2n/(3n+1)]BnAn-1=[2n/(3n+1)]Bn-1lim(n→∞)an/bn=lim(n→∞)[An-An-1]/[Bn-Bn-1]=lim(n→∞)[2n/(3n+1)][Bn
求数列{an}前n项的和,常用的方法就是裂项相消法.因为an=n(n+1)=n(n+1)[(n+2)-(n-1)]/3=[n(n+1)(n+2)-(n-1)n(n+1)]/3=(1/3)[-(n-1)
an看做两个数列,其中n^2求和根据平方数列求和公式为:n(n+1)(2n+1)/6n求和根据等差数列求和公式为:(1+n)*n/2两者相加即为答案
(1)当n≥2时,an=Sn-Sn-1=n(2n-1)-(n-1)(2n-3)=4n-3,当n=1时,a1=S1=1,适合.∴an=4n-3,∵an-an-1=4(n≥2),∴an为等差数列.(2)由
(1)Sn=n^2-10nan=Sn-S(n-1)=(2n-1)-10=2n-11=>{an}是等差娄列(2)bn=(an+1)/an=(2n-10)/(2n-11)maxbn=b1=8/9minbn
an=Sn-Sn-1=1/3n(n+1)(n+2)-1/3n(n+1)(n-1)=n(n+1)所以1/an=1/n(n+1)=1/n-1/n+1数列(1/an)的前n项和=1-1/2+1/2-1/3+
Sn=(-1)^n(2n^2+4n+1)-1Sn-1=(-1)^(n-1)[2(n-1)^2+4(n-1)+1]-1an=Sn-Sn-1=(-1)^n(4n^2+4n)bn=1/(4n^2+4n)=1
an就已求错了.Sn=(-1)^n(2n^2+4n+1)-1S(n-1)=(-1)^(n-1)*[2(n-1)^2+4(n-1)+1]-1=-(-1)^n(2n^2-1)-1an=Sn-S(n-1)=
(1)令n=1a1=S1=32-1+1=32Sn=32n-n²+1Sn-1=32(n-1)-(n-1)²+1an=Sn-Sn-1=32n-n²+1-32(n-1)+(n-
(1)Sn=1*3*5+3*5*7+5*7*9+……+(2n-1)(2n+1)(2n+3)=1*3*5+1/8*(3*5*7*9-1*3*5*7)+1/8*(5*7*9*11-3*5*7*9)+……+
【方法1:强行展开a(n)表达式】1+2+……+n=n(n+1)/21^2+2^2+……+n^2=n(n+1)(2n+1)/61^3+2^3+……+n^3=n^2(n+1)^2/41^4+2^4+……
2Sn=(n+1)an2S(n-1)=na(n-1)两式相减得2an=(n+1)an-na(n-1)移相得(1-n)an=-na(n-1)得an=(n/(n-1))a(n-1)an=(n/(n-1))
Sn=10n-n²,a1=S1=9,n≥2时,an=Sn-S(n-1)=11-2n∴an=11-2n(n≥1)该数列前5项为正,从第6起为负.①1≤n≤5时,Bn=Sn=10n-n²
若n=2kSn=(4+3(2k-1)+1)/2+2^k-2=2^k+3k-1=2^(n/2)+3n/2-1若n=2k+1Sn=2^k+3k-1+3(2k+1)+1=2^k+9k+3=2^((n-1)/
/>n≥2时,an=Sn/n+2(n-1)Sn=nan-2n(n-1)S(n-1)=(n-1)an-2(n-1)(n-2)Sn-S(n-1)=an=nan-2n(n-1)-(n-1)an+2(n-1)
S[n]=n-5a[n]-85其中:为了表示清楚,[n]表示下标,S[n-1]=n-1-5a[n-1]-85两式相减:a[n]=1+5(a[n-1]-a[n])a[n]-1=5(a[n-1]-1)-5
an=1/(√(n+2)+√n)=[√(n+2)-√n]/[(√(n+2)+√n)(√(n+2)-√n)]=[√(n+2)-√n]/(n+2)-n)=[√(n+2)-√n]/22an=√(n+2)-√