Posted: Wed Sep 22, 2004 6:43 am    Post subject: Is the limit of following sequence equal to pi?

Denote a_i = the i_th digit of pi a_1 = 3 a_2 = 1 … Let r_i = r_(i-1)+a_i/(10)^(i-1) (for i>= 2) r_1 = 3 r_2 = 3.1 r_3 = 3.14 So…Is Lim (r_n) = pi?_________________人生三大無奈: 搵食ja 犯法呀

我想ga

Posted: Wed Sep 22, 2004 9:16 am    Post subject:

Of course[unparseable or potentially dangerous latex formula]
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Posted: Wed Sep 22, 2004 10:26 pm    Post subject:

THX! I am also working on another prob. Is that possible for a sequence {X_n} that X_i is irrational… but the lim (X_n) is rational?_________________人生三大無奈: 搵食ja 犯法呀

我想ga

Posted: Thu Sep 23, 2004 1:50 pm    Post subject: Limit

Definitely you can do so:
As in your previous message, we know .
Therefore for any rational , we have , and is an irrational sequence._________________

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