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tough137
Joined: 20 Apr 2004Posts: 10

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_(i1)+a_i/(10)^(i1) (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





aRdolf
Frequent VisitorJoined: 18 Jan 2004Posts: 37

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



Of course[unparseable or potentially dangerous latex formula]
,





tough137
Joined: 20 Apr 2004Posts: 10

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
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Peter
Frequent VisitorJoined: 18 Jan 2004Posts: 115
Location: Hong Kong

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._________________
Therefore do not worry about tomorrow, for tomorrow will worry about itself. Each day has enough trouble of its own.





