For which parameter this kind of series converges
up vote
-2
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The sum is the following:
$sum_{k=1}^{infty}frac{a}{k^b}$
For which parameters this serie converges(a and b)?
convergence
asked Nov 26 at 4:44
user587779
94
add a comment |
up vote
-2
down vote
favorite
The sum is the following:
$sum_{k=1}^{infty}frac{a}{k^b}$
For which parameters this serie converges(a and b)?
convergence
asked Nov 26 at 4:44
user587779
94
what have you tried? what result do you know that can possibly solve the problem?
– Siong Thye Goh
Nov 26 at 4:48
add a comment |
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
The sum is the following:
$sum_{k=1}^{infty}frac{a}{k^b}$
For which parameters this serie converges(a and b)?
convergence
asked Nov 26 at 4:44
user587779
94
The sum is the following:
$sum_{k=1}^{infty}frac{a}{k^b}$
For which parameters this serie converges(a and b)?
convergence
convergence
asked Nov 26 at 4:44
user587779
94
asked Nov 26 at 4:44
user587779
94
asked Nov 26 at 4:44
user587779
94
asked Nov 26 at 4:44
user587779
94
asked Nov 26 at 4:44
user587779
94
94
what have you tried? what result do you know that can possibly solve the problem?
– Siong Thye Goh
Nov 26 at 4:48
add a comment |
what have you tried? what result do you know that can possibly solve the problem?
– Siong Thye Goh
Nov 26 at 4:48
what have you tried? what result do you know that can possibly solve the problem?
– Siong Thye Goh
Nov 26 at 4:48
what have you tried? what result do you know that can possibly solve the problem?
– Siong Thye Goh
Nov 26 at 4:48
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
accepted
One may apply the integral test to $displaystyle f(x):=frac{a}{x^b}$,
$$
int_1^N f(x),dxlesum_{k=1}^N f(k)le f(1)+int_1^N f(x),dx,qquad N>1,
$$ and see it converges iff $,b>1$.
answered Nov 26 at 4:51
Olivier Oloa
107k17175293
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
One may apply the integral test to $displaystyle f(x):=frac{a}{x^b}$,
$$
int_1^N f(x),dxlesum_{k=1}^N f(k)le f(1)+int_1^N f(x),dx,qquad N>1,
$$ and see it converges iff $,b>1$.
answered Nov 26 at 4:51
Olivier Oloa
107k17175293
add a comment |
up vote
0
down vote
accepted
One may apply the integral test to $displaystyle f(x):=frac{a}{x^b}$,
$$
int_1^N f(x),dxlesum_{k=1}^N f(k)le f(1)+int_1^N f(x),dx,qquad N>1,
$$ and see it converges iff $,b>1$.
answered Nov 26 at 4:51
Olivier Oloa
107k17175293
add a comment |
up vote
0
down vote
accepted
up vote
0
down vote
accepted
One may apply the integral test to $displaystyle f(x):=frac{a}{x^b}$,
$$
int_1^N f(x),dxlesum_{k=1}^N f(k)le f(1)+int_1^N f(x),dx,qquad N>1,
$$ and see it converges iff $,b>1$.
answered Nov 26 at 4:51
Olivier Oloa
107k17175293
One may apply the integral test to $displaystyle f(x):=frac{a}{x^b}$,
$$
int_1^N f(x),dxlesum_{k=1}^N f(k)le f(1)+int_1^N f(x),dx,qquad N>1,
$$ and see it converges iff $,b>1$.
answered Nov 26 at 4:51
Olivier Oloa
107k17175293
edited Nov 26 at 4:56
answered Nov 26 at 4:51
Olivier Oloa
107k17175293
answered Nov 26 at 4:51
Olivier Oloa
107k17175293
answered Nov 26 at 4:51
Olivier Oloa
107k17175293
107k17175293
add a comment |
add a comment |
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what have you tried? what result do you know that can possibly solve the problem?
– Siong Thye Goh
Nov 26 at 4:48