## 295 Reputation

16 years, 206 days

## Complex instruction...

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.

## Database...

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

## Database...

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

## Thanks...

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

## Thanks...

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

## Does not work for p>6...

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

## Does not work for p>6...

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

## I see...

Oh! Yes. I got it. Thanks.

## I see...

Oh! Yes. I got it. Thanks.

## What does it mean?...

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

## What does it mean?...

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

## plot series...

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.

## plot series...

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.

## A series problem...

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]);

## A series problem...

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]);

 1 2 3 4 5 6 7 Page 3 of 7
﻿