Sum of the series $sumlimits_{n=1}^infty frac{x^{2n}}{ncdot2^n}$
$$sum_{n=1}^infty frac{x^{2n}}{ncdot2^n}=?$$
I can find $$sum_{n=1}^infty frac{x^{n}}{ncdot2^n}$$,but how i get $x^{2n}$ from that?
sequences-and-series
edited Nov 25 at 17:56
Did
246k23220454
asked May 19 '14 at 12:43
user128576
905
add a comment |
$$sum_{n=1}^infty frac{x^{2n}}{ncdot2^n}=?$$
I can find $$sum_{n=1}^infty frac{x^{n}}{ncdot2^n}$$,but how i get $x^{2n}$ from that?
sequences-and-series
edited Nov 25 at 17:56
Did
246k23220454
asked May 19 '14 at 12:43
user128576
905
1
Replace $x$ by $x^2$.
– David
May 19 '14 at 12:45
This is a polylogarithm.
– Lucian
May 19 '14 at 12:51
we didn't learn about special functions(maybe we mentioned one or two...),but i can replace x with everything,that makes no problem?
– user128576
May 19 '14 at 12:58
@Lucian Sure, with poly = mono...
– Did
May 19 '14 at 13:00
add a comment |
$$sum_{n=1}^infty frac{x^{2n}}{ncdot2^n}=?$$
I can find $$sum_{n=1}^infty frac{x^{n}}{ncdot2^n}$$,but how i get $x^{2n}$ from that?
sequences-and-series
edited Nov 25 at 17:56
Did
246k23220454
asked May 19 '14 at 12:43
user128576
905
$$sum_{n=1}^infty frac{x^{2n}}{ncdot2^n}=?$$
I can find $$sum_{n=1}^infty frac{x^{n}}{ncdot2^n}$$,but how i get $x^{2n}$ from that?
sequences-and-series
sequences-and-series
edited Nov 25 at 17:56
Did
246k23220454
asked May 19 '14 at 12:43
user128576
905
edited Nov 25 at 17:56
Did
246k23220454
asked May 19 '14 at 12:43
user128576
905
edited Nov 25 at 17:56
Did
246k23220454
edited Nov 25 at 17:56
Did
246k23220454
edited Nov 25 at 17:56
Did
246k23220454
246k23220454
asked May 19 '14 at 12:43
user128576
905
asked May 19 '14 at 12:43
user128576
905
asked May 19 '14 at 12:43
user128576
905
905
1
Replace $x$ by $x^2$.
– David
May 19 '14 at 12:45
This is a polylogarithm.
– Lucian
May 19 '14 at 12:51
we didn't learn about special functions(maybe we mentioned one or two...),but i can replace x with everything,that makes no problem?
– user128576
May 19 '14 at 12:58
@Lucian Sure, with poly = mono...
– Did
May 19 '14 at 13:00
add a comment |
1
Replace $x$ by $x^2$.
– David
May 19 '14 at 12:45
This is a polylogarithm.
– Lucian
May 19 '14 at 12:51
we didn't learn about special functions(maybe we mentioned one or two...),but i can replace x with everything,that makes no problem?
– user128576
May 19 '14 at 12:58
@Lucian Sure, with poly = mono...
– Did
May 19 '14 at 13:00
1
1
Replace $x$ by $x^2$.
– David
May 19 '14 at 12:45
Replace $x$ by $x^2$.
– David
May 19 '14 at 12:45
This is a polylogarithm.
– Lucian
May 19 '14 at 12:51
This is a polylogarithm.
– Lucian
May 19 '14 at 12:51
we didn't learn about special functions(maybe we mentioned one or two...),but i can replace x with everything,that makes no problem?
– user128576
May 19 '14 at 12:58
we didn't learn about special functions(maybe we mentioned one or two...),but i can replace x with everything,that makes no problem?
– user128576
May 19 '14 at 12:58
@Lucian Sure, with poly = mono...
– Did
May 19 '14 at 13:00
@Lucian Sure, with poly = mono...
– Did
May 19 '14 at 13:00
add a comment |
1 Answer
1
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(2018-11-25) "Amusing" revenge downvote, four years later.
You know that
$$sum_{ngeqslant1}frac1nt^n=-log(1-t)
$$
and you are asking about
$$sum_{ngeqslant1}frac{x^{2n}}{n2^n}=sum_{ngeqslant1}frac1nleft(frac{x^2}2right)^n=-logleft(1-ldotsright).
$$
answered May 19 '14 at 13:00
Did
246k23220454
add a comment |
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1 Answer
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active
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
(2018-11-25) "Amusing" revenge downvote, four years later.
You know that
$$sum_{ngeqslant1}frac1nt^n=-log(1-t)
$$
and you are asking about
$$sum_{ngeqslant1}frac{x^{2n}}{n2^n}=sum_{ngeqslant1}frac1nleft(frac{x^2}2right)^n=-logleft(1-ldotsright).
$$
answered May 19 '14 at 13:00
Did
246k23220454
add a comment |
(2018-11-25) "Amusing" revenge downvote, four years later.
You know that
$$sum_{ngeqslant1}frac1nt^n=-log(1-t)
$$
and you are asking about
$$sum_{ngeqslant1}frac{x^{2n}}{n2^n}=sum_{ngeqslant1}frac1nleft(frac{x^2}2right)^n=-logleft(1-ldotsright).
$$
answered May 19 '14 at 13:00
Did
246k23220454
add a comment |
(2018-11-25) "Amusing" revenge downvote, four years later.
You know that
$$sum_{ngeqslant1}frac1nt^n=-log(1-t)
$$
and you are asking about
$$sum_{ngeqslant1}frac{x^{2n}}{n2^n}=sum_{ngeqslant1}frac1nleft(frac{x^2}2right)^n=-logleft(1-ldotsright).
$$
answered May 19 '14 at 13:00
Did
246k23220454
(2018-11-25) "Amusing" revenge downvote, four years later.
You know that
$$sum_{ngeqslant1}frac1nt^n=-log(1-t)
$$
and you are asking about
$$sum_{ngeqslant1}frac{x^{2n}}{n2^n}=sum_{ngeqslant1}frac1nleft(frac{x^2}2right)^n=-logleft(1-ldotsright).
$$
answered May 19 '14 at 13:00
Did
246k23220454
edited Nov 25 at 17:55
answered May 19 '14 at 13:00
Did
246k23220454
answered May 19 '14 at 13:00
Did
246k23220454
answered May 19 '14 at 13:00
Did
246k23220454
246k23220454
add a comment |
add a comment |
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1
Replace $x$ by $x^2$.
– David
May 19 '14 at 12:45
This is a polylogarithm.
– Lucian
May 19 '14 at 12:51
we didn't learn about special functions(maybe we mentioned one or two...),but i can replace x with everything,that makes no problem?
– user128576
May 19 '14 at 12:58
@Lucian Sure, with poly = mono...
– Did
May 19 '14 at 13:00