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how to solve equation like,sin(x)=exp(x)?AND can we put x=log[sin(x)]?thank you Husseinshimaljasimdini ( talk) 11:18, 4 April 2008 (UTC)
I'm looking for a convergent series with positive terms, other than a geometric series or a telescoping series, which converges to a nice value and whose partial sums are also nicely expressible. Does anyone have any examples of series like this? — Bkell ( talk) 16:59, 4 April 2008 (UTC)
Hi. Now, before you freak about its easiness, let me explain. I know how to do some infinite series of decimals. For example, 0.33333... is 1/3, 0.090909... is 1/11, 0.166666... is 1/6, 0.11111... is 1/9, 0.22222... is 2/9, 0.99999... is 1, and so on. Other ones, like 0.363636... are calculatable by dividing 1 by that number (1/2.75 = 4/11), and other ones like 0.181818..., 0.833333..., and 1.55555... are easy because they're based on the above numbers. However, is there a quick way, other than rounding, truncating, estimating, and making the denominator infinity, to make a number that produces a very long series of decimals when you divide it into 1, and is a repeat of a prime number, into a fraction? For example, 0.23232323... . Or, can it be possible for a repeating series to be irrational, or can only non-repeating series like 3.1415926535897932384626433832... be irrational? I'm not asking for the answer to a specific question, just if there is a way to do this accurately, or is rounding/truncating better? Thanks. ~ A H 1( T C U) 21:14, 4 April 2008 (UTC)
My favorite way to do this is to treat the fraction as the sum of an infinite Geometric Series, which off the top of my head, I don't remember exactly, but the idea is this: .11111111 is 1*.1 + 1*.01 + 1*.001, etc. -- Arcoain ( talk) 00:36, 8 April 2008 (UTC)
Mathematics desk | ||
---|---|---|
< April 3 | << Mar | April | May >> | April 5 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
how to solve equation like,sin(x)=exp(x)?AND can we put x=log[sin(x)]?thank you Husseinshimaljasimdini ( talk) 11:18, 4 April 2008 (UTC)
I'm looking for a convergent series with positive terms, other than a geometric series or a telescoping series, which converges to a nice value and whose partial sums are also nicely expressible. Does anyone have any examples of series like this? — Bkell ( talk) 16:59, 4 April 2008 (UTC)
Hi. Now, before you freak about its easiness, let me explain. I know how to do some infinite series of decimals. For example, 0.33333... is 1/3, 0.090909... is 1/11, 0.166666... is 1/6, 0.11111... is 1/9, 0.22222... is 2/9, 0.99999... is 1, and so on. Other ones, like 0.363636... are calculatable by dividing 1 by that number (1/2.75 = 4/11), and other ones like 0.181818..., 0.833333..., and 1.55555... are easy because they're based on the above numbers. However, is there a quick way, other than rounding, truncating, estimating, and making the denominator infinity, to make a number that produces a very long series of decimals when you divide it into 1, and is a repeat of a prime number, into a fraction? For example, 0.23232323... . Or, can it be possible for a repeating series to be irrational, or can only non-repeating series like 3.1415926535897932384626433832... be irrational? I'm not asking for the answer to a specific question, just if there is a way to do this accurately, or is rounding/truncating better? Thanks. ~ A H 1( T C U) 21:14, 4 April 2008 (UTC)
My favorite way to do this is to treat the fraction as the sum of an infinite Geometric Series, which off the top of my head, I don't remember exactly, but the idea is this: .11111111 is 1*.1 + 1*.01 + 1*.001, etc. -- Arcoain ( talk) 00:36, 8 April 2008 (UTC)