求无穷级数 1/10+1/10^2+2/10^3+3/10^4+5/10^5+8/10^6+… 之和

王守恩

求和：1/10+1/100+2/1000+3/10000+...

luyuanhong

luyuanhong

王守恩

蔡家雄 发表于 2017-11-19 20:25
兔子数列中的难题

1/1+1/1+1/2+1/3+1/5+1/8+1/13+1/21+1/34+1/55+1/89+1/144+...... = ?

兔子数列中的难题

朱明君

luyuanhong

蔡家雄 发表于 2017-11-21 19:20
证明：二项式系数平方的和等于 C(2n, n) = (2n)!/(n!)^2

王守恩

谢谢陆老师！！！谢谢elim！！！

\(\frac{1}{1}+\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{5}+\frac{1}{8}+\frac{1}{13}+\frac{1}{21}+\frac{1}{34}+\frac{1}{55}+\frac{1}{89}+\frac{1}{144}+\frac{1}{233}+\frac{1}{377}+\frac{1}{610}+\frac{1}{987}+...... = 3.359885666243177553172011302\)

\(\displaystyle\sum_{n=0}^{\infty}\frac{\sqrt{5}}{\cos(n\pi)\phi^{2n+1}-1}\)

3.3598856662431775531720113029189271796889051337319684864955538153251303189966833836154162164567900872970453429288539133041367890171008836795913517330771190785803335503
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