MaplePrimes - answers and comments on Question, int is not equal to add - why ?

why should it?

Scott03 — Tue, 11 May 2010 17:20:00 Z

Both are different techniques. As an example, take the first part of the equation you are using

p^n*2^(n-1)

This simplifies down to 0.5 with your numbers. So when you add 0.5 from n=1 to 7, then maple will be adding 0.5 seven times (n=1,2,3,...,7). As for the integration, this is usually viewed as area under the curve, so in this case you are finding the area of a rectangle with the width 0.5 and length 6. Therefore the sumation will produce 3.5 and integration 3.0. This is likely why you are getting different results

Scott

ok, thanx. Yes, you might be

alex_01 — Tue, 11 May 2010 17:45:37 Z

ok, thanx. Yes, you might be right. I forgot that you lose 1 on the length ie 0.5*( 7-1) =0.5*6 =3.
It would have been easier though if the length would have been the same ie
a starting point of zero ie 0.5*( 7-0) =0.5*7 =3.5 but then I guess add would produce 4 humm..

but that is another

alex_01 — Tue, 11 May 2010 17:52:57 Z

but that is another thing:

add(.5, x = 0 .. 7);
4.0
0.5*7;
3.5
??

n+1

Scott03 — Tue, 11 May 2010 17:58:00 Z

You have to watch out for the number of times add will add the numbers. It will take the very first location (here x=0) then at every integer value between and including the end point of your interval. So both ends of the interval will be included in the sumation if they are integers.

*edit: I had at first thought that if you wanted to remove the beginning of the sumation that you only needed to change the range to x=0.01..7, but I was incorrect. To see what is going on try the following

add(f(x),x=0..7);

add(f(x),x=0.1..7);

Scott

With second thought it kind

alex_01 — Tue, 11 May 2010 18:18:22 Z

With second thought it kind of make sense to have add(0.5, x = 0 .. 7) = 4.0
Since a 0.5 line has a value of 0.5 at 0 ie add(0.5, x = 0 .. 7) = add(0.5, x = 1 .. 8) = 4.0
I am not completely comfortable with that int<> add but I might get over it :-)

counts, inclusive

pagan — Wed, 12 May 2010 01:16:47 Z

The number of integers between integers A and B, inclusive, is B-A+1.

So between 0 and 7, inclusive, there are eight integers.

You can check this by counting from 0 to 7 on your fingers. If that is confusing, then try it first from 1 to 8. And then think about why that is the same as counting from 0 to 7.

Hence

> add(0.5,x=0..7);
                                      4.0
 
> add(0.5,x=1..8);
                                      4.0
 
> 0.5*8;
                                      4.0