这个N项和有公式吗

mathe

在$1<x<=exp(1/e)$时y是存在的，只是需要证明，证明很简单，归纳证明对于这个范围的x,$x^{x^...}$有限次都小于对应的y而且单调增就可以了

wayne

11# mathe
那么 x=1.01时，y等于多少

==========================
{1.01, 1.0101, 1.0102, 1.01031, 1.01041, 1.01052, 1.01063, 1.01075, \
1.01086, 1.01098, 1.0111, 1.01123, 1.01136, 1.01149, 1.01162, \
1.01175, 1.01189, 1.01203, 1.01218, 1.01233, 1.01248, 1.01264, \
1.0128, 1.01297, 1.01313, 1.01331, 1.01349, 1.01367, 1.01386, \
1.01405, 1.01425, 1.01445, 1.01466, 1.01488, 1.0151, 1.01533, \
1.01557, 1.01582, 1.01607, 1.01633, 1.0166, 1.01687, 1.01716, \
1.01746, 1.01777, 1.01809, 1.01842, 1.01876, 1.01911, 1.01948, \
1.01986, 1.02026, 1.02068, 1.02111, 1.02156, 1.02203, 1.02252, \
1.02303, 1.02357, 1.02413, 1.02472, 1.02534, 1.02599, 1.02668, \
1.0274, 1.02816, 1.02896, 1.02982, 1.03072, 1.03168, 1.0327, 1.03378, \
1.03494, 1.03619, 1.03752, 1.03896, 1.0405, 1.04218, 1.044, 1.04597, \
1.04814, 1.05051, 1.05313, 1.05603, 1.05926, 1.06288, 1.06697, \
1.07161, 1.07693, 1.08309, 1.09029, 1.09884, 1.10912, 1.12173, \
1.13752, 1.15786, 1.18496, 1.22275, 1.27876, 1.36949, 1.53821, \
1.93942, 3.61338, 103.741, 1.36781*10^209}

mathe

你算错了
1.01,1.010100503341741585660644791,1.010101513484671390425465593,1.010101523637460703659505973,1.010101523739504808825975866

wayne

13# mathe
的确错了。
一年前的我就错了，
错的如此简单而露骨。
直到现在才觉察。

为什么我会两次掉进同一个烂坑呢？
这是一个很严重而现实的问题。

谢谢mathe！谢谢mathe！

liexi20101117

看了上面几面老师提供的链接文章，很不错，再请问$x^{(1/x)^{x^...}}$这个的解又是如何的呢？