a*****y
发帖数: 33185 | |
r*****n
发帖数: 4844 | |
a*****y
发帖数: 33185 | 3 是多少你知道？
【在 r*****n 的大作中提到】
: 有
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r*****n
发帖数: 4844 | 4 不知道，列个公式算算嘛
【在 a*****y 的大作中提到】
: 是多少你知道？
|
a*****y
发帖数: 33185 | 5 哪有那么简单，肯定跟Pi有关，如果是分母是一次方或者二次方都有现成的结果，三次
方就搞不定了
【在 r*****n 的大作中提到】
: 不知道，列个公式算算嘛
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f***r
发帖数: 5548 | 6 这个跟算pi的哪个公式有点儿像，
如何判断级数是否收敛啊？需要微积分的知识吗？
偶得数学快忘光了。。。
【在 a*****y 的大作中提到】
: 这个级数有没有收敛值？
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a*****y
发帖数: 33185 | 7 http://en.wikipedia.org/wiki/Pi
Second millennium AD
Until the second millennium AD, estimations of π were accurate to fewer
than 10 decimal digits. The next major advances in the study of π came with
the development of infinite series and subsequently with the discovery of
calculus, which permit the estimation of π to any desired accuracy by
considering sufficiently many terms of a relevant series. Around 1400,
Madhava of Sangamagrama found the first known such series:
{\pi} = 4\sum^\infty_{k=0} \frac{(-1)^k}{2k+1} = \frac{4}{1} - \frac{4}{
3} + \frac{4}{5} - \frac{4}{7} + \frac{4}{9} - \frac{4}{11} + \cdots.\!
This is now known as the Madhava–Leibniz series[55][56] or Gregory–Leibniz
series since it was rediscovered by James Gregory and Gottfried Leibniz in
the 17th century.
【在 f***r 的大作中提到】
: 这个跟算pi的哪个公式有点儿像，
: 如何判断级数是否收敛啊？需要微积分的知识吗？
: 偶得数学快忘光了。。。
|
a*****y
发帖数: 33185 | 8 关于π的一个古典级数是1674年发现的Leibniz级数：
π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + …
with
}{
【在 a*****y 的大作中提到】
: http://en.wikipedia.org/wiki/Pi
: Second millennium AD
: Until the second millennium AD, estimations of π were accurate to fewer
: than 10 decimal digits. The next major advances in the study of π came with
: the development of infinite series and subsequently with the discovery of
: calculus, which permit the estimation of π to any desired accuracy by
: considering sufficiently many terms of a relevant series. Around 1400,
: Madhava of Sangamagrama found the first known such series:
: {\pi} = 4\sum^\infty_{k=0} \frac{(-1)^k}{2k+1} = \frac{4}{1} - \frac{4}{
: 3} + \frac{4}{5} - \frac{4}{7} + \frac{4}{9} - \frac{4}{11} + \cdots.\!
|
