apologize timbaland歌詞

"Apologize" 是由 Timbaland 製作、Pink 演唱的一首歌曲。歌詞如下：

I'm sorry for being such a fan

Sorry for the fan, the fan, fan, fan

If I could take it back

But I won't resign

Your friendship man, that I left and thought it's dead and gone

It seems to grow back when I'm not around it, to find

Apologize

So, just like that you drop it and give up the love we worked up

Apologize

So I'm asking you to take it back and give it up

Sorry for the time that I was so insecure

Sorry for the insecure, the insecure, sec, sec

If I could erase it all

But I know that I can't change it all

So I apologize for being so out of control, oh

But when I get emotional you ain't the type to call it like it is

I apologize

So just like that you drop it and give up the love we worked up

Apologize

So I'm asking you to take it back and give it up up up up up up up up up up up up up up up up up

Come on and get with it, so what's your excuse? (your excuse)

And what could you possibly feel that could make you give me no contact? (contact)

What would make you leave your heart? (your heart) and so insecure? (secure) like I was Mr. Security? (I don't know)

And I apologize for being so unpredictable (predictable)

So just like that you drop it and give up the love we worked up (worked up)

Apologize (apologize)

So I'm asking you to take it back and give it up (give it up) up up up up up up up (don't have to justify, yeah yeah yeah yeah) up up up up up up

Get back together (back together) all we do is argue and so at ease now將數列{a[n]}按一定規則進行分組求和，使得每組的首項為2，公差為-2，其餘項都為6，當組數n趨近於無窮大時，求所有組數的和。

我們可以通過觀察規律，發現數列的分組情況如下：第一組：2第二組：-6，-4第三組：12，6，-18第四組：-30，-18，-6，60第五組：-90，-66，-30，36，90\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots第一組和為：$2 = 2 \times 1$第二組和為：$-6 - 4 = -10 = 2 \times 5$第三組和為：$12 + 6 - 18 = 0 = 2 \times (5+7)$以此類推可知每一組的和均為常數因此總和就是第一組的和加上其餘各組的和(其中首項不變)。設第一組為首項為$x$的等差數列前$n$項和，其餘項每組的和為常數項（首項均為$2$），可得：$S_{n} = xn + \frac{n(n - 1)}{2} \times ( - 2) + \frac{(n - 1)(n - 2)}{2} \times 6$$= xn + ( - 2n^{2} + n + 3n^{2} - 3n) \times 6$$= xn + 3(n - \frac{1}{2})^{2} \times 6$$= 3(n + \frac{1}{4})^{2} \times 6$當組數$n$趨近於無窮大時，總和就是：$S = S_{n \longrightarrow \infty}$$= \lim_{n \longrightarrow \infty}3(\frac{n + \frac{1}{4}}{2})^{2} \times 6$$= \lim_{n \longrightarrow \infty}(\frac{5n + 1}{4})^{2} \times 3$$= (\