scumath

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16 years, 31 days

MaplePrimes Activity


These are replies submitted by scumath

Thanks for your comments. But I couldn't follow the instruction. It is too complex for me. I hoped the Maple software itself can solve the problem I have, but I was wrong.

Thanks. But I don't know how to use the Database.

Thanks. But I don't know how to use the Database.

Wonderful!  Thanks a lot.

p:=16:
f:= sum(1/n^p,n=x+1..infinity): asympt(f,x,20);

                 1        1         4      34            1
               ------ - ----- + ----- - ----- + O(---)
                     15      16      17     19      20
               15 x     2 x     3 x     5 x           x


 

Wonderful!  Thanks a lot.

p:=16:
f:= sum(1/n^p,n=x+1..infinity): asympt(f,x,20);

                 1        1         4      34            1
               ------ - ----- + ----- - ----- + O(---)
                     15      16      17     19      20
               15 x     2 x     3 x     5 x           x


 

Then I use your code to other p-series. But it does not work for p>6. 

p:=5:
f:= sum(1/n^p,n=x+1..infinity): asympt(f,x);

                         1      1             1
                        ----  -  ---- + O(----)
                             4      5           6
                        4 x    2 x           x

p:=6:
f:= sum(1/n^p,n=x+1..infinity): asympt(f,x);

                              1           1
                            ---- + O(----)
                                 5          6
                            5 x           x

 

But
p:=7:
f:= sum(1/n^p,n=x+1..infinity): asympt(f,x);

                                     1
                               O(----)
                                       6
                                     x
 

 

Then I use your code to other p-series. But it does not work for p>6. 

p:=5:
f:= sum(1/n^p,n=x+1..infinity): asympt(f,x);

                         1      1             1
                        ----  -  ---- + O(----)
                             4      5           6
                        4 x    2 x           x

p:=6:
f:= sum(1/n^p,n=x+1..infinity): asympt(f,x);

                              1           1
                            ---- + O(----)
                                 5          6
                            5 x           x

 

But
p:=7:
f:= sum(1/n^p,n=x+1..infinity): asympt(f,x);

                                     1
                               O(----)
                                       6
                                     x
 

 

Oh! Yes. I got it. Thanks.

Oh! Yes. I got it. Thanks.

But it is hard for me to understand your comment. How is it related to my problem?

But it is hard for me to understand your comment. How is it related to my problem?

Thank you for your good suggestions.
I think "f := x-> sum(1/n^2,n=x+1..infinity); plot(f,1..5);" is what I need.

Thank you for your good suggestions.
I think "f := x-> sum(1/n^2,n=x+1..infinity); plot(f,1..5);" is what I need.

Thank you so much. Both commands work quite well.
Now I can use the graph to check the following fact:


with(plots):X:=50:
f:= x -> sum(1/n^2,n=ceil(x)..infinity):
A:=plot(f(x),x=1..X,thickness=2):
B:=plot(1/x,x=1..X,color=blue,thickness=2):
display(A,B,view=[-1..X,0..1]);

Thank you so much. Both commands work quite well.
Now I can use the graph to check the following fact:


with(plots):X:=50:
f:= x -> sum(1/n^2,n=ceil(x)..infinity):
A:=plot(f(x),x=1..X,thickness=2):
B:=plot(1/x,x=1..X,color=blue,thickness=2):
display(A,B,view=[-1..X,0..1]);

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