- #36
dilan
- 72
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Well it say the number = y
and |y|<1
then the product will be less than the number right?
and |y|<1
then the product will be less than the number right?
[tex]\sum_{i = m} ^ n[/tex], this is the summation symbol. It's a capital Sigma.dilan said:Ya right. 1 is the bound because if it gose beyond 1 then we won't find a bound because we can get large numbers right?
Anyway this is the first time I used this symbol next to the "Sn ="
Can you teach me about this also?
[tex]S=\sum_{n=0}^{\infty}x^{n}[/tex]
arildno said:So, what we have found out, is that the INFINITE series,
[tex]S=\sum_{n=0}^{\infty}x^{n}[/tex]
is a meaningful concept, as long as |x|<1.
We call 1 here to be the radius of convergence for the infinite series, that is the bound we must put on x, in order for the infinite series to have any meaning (I.e, being some number).
Okay?
Have you learned limit by the way? Something looks like:dilan said:But I don't know anything about this
[tex]\lim_{N \rightarrow \infty} S_N = L, \ N \in \mathbb{N}[/tex]
arildno said:Hmm..I just reviewed your original question:
It seems to want the general termof the expansion, rather than the specific one.
1.Have you learned about the Cauchy product of series yet?
2. Have you learned about Taylorseries, and how to compute them?
arildno said:Seems that you've got a tough time ahead, but the right attitude to face it then!
Now, have you learned that a function f(x) may be written in series form:
[itex]f(x)=f(0)+f'(0)x+f''(0)\frac{x^{2}}{1*2}+f'''(0)\frac{x^{3}}{1*2*3}+++[/tex]
where, say, f''(0) means the 2nd derivative of f, evaluated at x=0?