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?
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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。。。
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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.\!
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