Question

已知数列{An} {Bn}中，a1=b1=1，An+1=Bn+n，Bn+1=An+(-1)^n，n∈N* ~~高手求解

已知数列{An} {Bn}中，a1=b1=1，An+1=Bn+n，Bn+1=An+(-1)^n，n∈N* 求证 A2n=n^2+n (注：An+1、A2n 、Bn+1 都是下标）
请给详细解答，拜托了~~

Answer 1

用数学归纳法：

1） 首先，当 n=1 时 A2 = 1^ + 1 = 2 ( 成立，因为 An+1=Bn+n ）

2） 现在证 若当 n=k 时 A2 k = k^2 + k 成立，则
当 n=k+1 时 A2（k+1）= （k+1）^2 + （k+1）也成立则可

A2（k+1）= B(2k+1) + (2k+1)
= A(2k) + (-1)^2k + (2k+1)
= A(2k) + 2k + 2
= k^2 + k + 2k + 2

=（k+1）^2 + （k+1）

成立！

Answer 2

a(n+1)=bn+n,b(n+1)=an+(-1)^n
bn=a(n-1)+(-1)^(n-1)=a(n-1)-(-1)^n
a(n+1)=a(n-1)-(-1)^n+n
即：a(n+1)-a(n-1)=n-(-1)^n
所以令n=3,5,7,……，2n-1时有：
a4-a2=3+1=4
a6-a4=5+1=6
a8-a6=7+1=8
……………
a2n-a(2n-2)=2n
以上(n-1)个式子左右分别相加：
a2n-a2=（4+6+……+2n)=n^2+n-2
a2=b1+1=2
a2n=n^2+n

Answer 3

. . . . . -

here not just because you wronged him on the phone over there yelling; -

love is two things. If he is not worthy of your love,cheap manolo blahnik sandals, then let go and give you the opportunity to each person the pursuit of happiness; if he is worthy of your love, then certainly his heart to love him and care for him,christian louboutin pumps uk, waiting for him! -

when he got too busy over and over again not to call just to tell him you want him; -

Do not lie to him, never. -

but if a boy can do the following that, he really loves you! -

boys willing to spend money on you, he does not love you! Boys cry for you,christian louboutin boots on sale, he does not love you! Boys die for you, not necessarily love you ... -

Oh,manolo blahnik sandals uk, to turn reading the

When a boy because you suffered the same pain and howl like a child; -

Do not have any male friends out of people, even if he can not see; -

Do not lie to him. If he really loves you, he can forgive all your mistakes, but can not forgive your lies. -

nasty when a boy clutching your hand around your campus to go round and round, just to let everyone know that you are his girlfriend, do not call your idea; -

Do not hang his phone, no matter how angry you are. Let the most angry is a guy than let him find his girlfriend; -

When a guy is willing to fight for your happiness away, struggle, willing to accompany you whatever you like to go, do what you want to do any, then you love him in earnest, no matter how many people hurt you, you have only this one will love you, he innocently. -

when a boy opened his eyes to send text messages every morning and love you every night before bed and you did not forget to say good night; -

When a guy is willing at any time, any place as you bend over to Department of loose shoelace; -

When a boy round the clock power, only to miss each of your phone, do not let you in any moment of a lost lonely; -

相关的主题文章：

An old satyr satyr gave the 40 small advice

N be a young, chairman of Advice

Let C drive to lose weight!