Finite series.... should this be easy?
Finite series.... should this be easy?
(OP)
Hi there,
I'm relativly new to mathcad and only been playign around with it fora couple of weeks. I've managed to get some examples and things from a friend to work through to help me, but i cant manage to create a program to find e to the x for an infinite series. Any help or examples would be great, i have this program so if you send an example you happen to have of this problem yourself for me to study (long shot??) that would be great! or an explination of how to tackle it is also brilliant.
Thanks Alot
Daniel
P.s. is there anyway of defining it till the value reaches a certain value of the previous? i.e. an eigth of the previous term? This is just purely out of interest so if its a bit tough no worries.
I'm relativly new to mathcad and only been playign around with it fora couple of weeks. I've managed to get some examples and things from a friend to work through to help me, but i cant manage to create a program to find e to the x for an infinite series. Any help or examples would be great, i have this program so if you send an example you happen to have of this problem yourself for me to study (long shot??) that would be great! or an explination of how to tackle it is also brilliant.
Thanks Alot
Daniel
P.s. is there anyway of defining it till the value reaches a certain value of the previous? i.e. an eigth of the previous term? This is just purely out of interest so if its a bit tough no worries.
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RE: Finite series.... should this be easy?
As a first step in looking up anything mathematics-related, I'd try googling for the term followed by "wolfram" so that you hit the Wolfram Mathworld site. I googled for "exponential function wolfram" and came up with:
htt
You can see there that e^x is defined as the sum from n=0 to infinity of (x^n)/n!.
So, to compute this in Mathcad, you need to:
-Click in a blank area
-Assign a value to x that you would like to calculate
-Choose the summation sign from the Calculus toolbar. Make sure you get the one that has 3 placeholders - 2 on the bottom for the variable and start value and 1 on the top for the stop value
-Enter n in the first placeholder on the bottom (for the variable)
-Enter 0 in the 2nd placeholder on the bottom (for the start value)
-Enter 10 (let's say) on the top placeholder (for the stop value)
-Then in the placeholder to the right of the summation, enter the expression x^n/n!.
-Then space until the cursor is highlighting the whole summation and hit equals. The result should be displayed.
Alternatively you could define an exponential function by setting the summation equal to something like exponential(x) on the left side of the assignment operator (by typing a colon.)
You can change the accuracy by changing the number 10. The higher you make it (i.e. the closer to infinity) you make it, the better the approximation. I doubt you'll need to go any higher than 20.
Just wondering...why not use the built-in exponential function? You can use it by just typing e^number or using exp(number).
Also, if you want to see the summation converge, you can always write a "program" to do it:
-Define a function
exponential(x,N)=sum from n=0 to N of (x^n)/n!
-Then define a range variable, i, that counts from 0 to 10 (or whatever you would like)
i:0,1;10
-Then assign values to the elements in an array
A[i : exponential(1.4,i)
(for example, to find the value of e^1.4 approximated)
-Print out the array
A=
Disclaimer: I just typed this up on a computer where I don't have Mathcad so I didn't try everything out. It should be close though.
HTH,
-Matt
RE: Finite series.... should this be easy?
Why did you point him to the Wolfram stuff? We're talking MathCad here, Mathmatica is another forum.
David