数列an满足a1=2,a(n+1)=an^2-n*an+1(n属于N*),(1)写出数列的前5项 (2)猜想并证明数列的通项公式通项公式是不是an=n+1,但是为什么我证明不了
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/20 08:33:01
![数列an满足a1=2,a(n+1)=an^2-n*an+1(n属于N*),(1)写出数列的前5项 (2)猜想并证明数列的通项公式通项公式是不是an=n+1,但是为什么我证明不了](/uploads/image/z/5089378-58-8.jpg?t=%E6%95%B0%E5%88%97an%E6%BB%A1%E8%B6%B3a1%3D2%2Ca%28n%2B1%29%3Dan%5E2-n%2Aan%2B1%28n%E5%B1%9E%E4%BA%8EN%2A%29%2C%281%29%E5%86%99%E5%87%BA%E6%95%B0%E5%88%97%E7%9A%84%E5%89%8D5%E9%A1%B9+%282%29%E7%8C%9C%E6%83%B3%E5%B9%B6%E8%AF%81%E6%98%8E%E6%95%B0%E5%88%97%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%E6%98%AF%E4%B8%8D%E6%98%AFan%3Dn%2B1%2C%E4%BD%86%E6%98%AF%E4%B8%BA%E4%BB%80%E4%B9%88%E6%88%91%E8%AF%81%E6%98%8E%E4%B8%8D%E4%BA%86)
xՒN@_ĴgZP##&IC *(.1F!AZ.߄t<f.Ϝ4W[|Ч`JdBYI
b7{U ɬaWdCV=|e3x|!*vAbۯVjzrrQsln_@^e:]ᇆXL(Z]A[lQ bhV]pPq< Z6P nG\AY
Pd5"
hx
0)+ c#+U/S6[LH̶o0g;$@&14fwPAF$31L'!AxI$W0E*x選z~p?Dk7K~-C
数列an满足a1=2,a(n+1)=an^2-n*an+1(n属于N*),(1)写出数列的前5项 (2)猜想并证明数列的通项公式通项公式是不是an=n+1,但是为什么我证明不了
数列an满足a1=2,a(n+1)=an^2-n*an+1(n属于N*),(1)写出数列的前5项 (2)猜想并证明数列的通项公式
通项公式是不是an=n+1,但是为什么我证明不了
数列an满足a1=2,a(n+1)=an^2-n*an+1(n属于N*),(1)写出数列的前5项 (2)猜想并证明数列的通项公式通项公式是不是an=n+1,但是为什么我证明不了
(1)
a1=2
a2=a1²-1×a1+1=4-2+1=3
a3=a2²-2×a2+1=9-6+1=4
a4=a3²-3×a3+1=16-12+1=5
a5=a4²-4×a4+1=25-20+1=6
(2)
猜想:an=n+1
证:
假设当n=k (k∈N+且k≥1)时,ak=k+1
则当n=k+1时,
a(k+1)=ak²-k×ak+1
=(k+1)²-k(k+1)+1
=k²+2k+1-k²-k+1
=k+2
=(k+1)+1
同样成立.
综上,得an=n+1
用数学归纳法很容易证明的.
数列{an}满足a1=2,a(n+1)=2an+n+2,求an
数列an满足a1=1,a(n+1)=an/[(2an)+1],求a2010
数列[An]满足a1=2,a(n+1)=3an-2 求an
数列{An}满足a1=1/2,a1+a2+..+an=n方an,求an
数列{an}满足a1=1 an+1=2n+1an/an+2n
已知数列{an}满足a(n+1)=an+n,a1=1,则an=
数列{an}满足a1=1,且an=an-1+3n-2,求an
已知数列{an}满足an+1=2an+3.5^n,a1=6.求an
已知数列an满足条件a1=-2 a(n+1)=2an/(1-an) 则an=
已知数列an满足a1=1,a(n+1)=an/(3an+2),则an=?
已知数列an满足a1=2,an=a(n-1)+2n,(n≥2),求an
已知数列an满足:a1=1,an-a(n-1)=n n大于等于2 求an
已知数列{an}满足a1=33,a(n+1)-an=2n,则an/n的最小值
已知数列{an}满足a1=33,a(n+1)-an=2n,求an/n的最小值
已知数列an满足a1=100,a(n+1)-an=2n,则(an)/n的最小值为
数列{an}满足a1=2,a(n+1)=-1/(an+1),则a2010等于
数列{an}满足a1=3,a n+1=2an,则a4等于
已知数列{an}满足a1=2,a(n+1)-an=a(n+1)*an,则a31=?