Summation using binomial theorem
0
$begingroup$
Find the sum $$sum_{x=1}^{m} Big(frac{2^x-1}{2^x}Big)^n$$ where $n$ belongs to natural number.
summation binomial-coefficients binomial-theorem
edited Jan 21 at 7:54
Shubham Johri
5,187717
asked Jan 21 at 7:27
user574937user574937
384
$endgroup$
add a comment |
0
$begingroup$
Find the sum $$sum_{x=1}^{m} Big(frac{2^x-1}{2^x}Big)^n$$ where $n$ belongs to natural number.
summation binomial-coefficients binomial-theorem
edited Jan 21 at 7:54
Shubham Johri
5,187717
asked Jan 21 at 7:27
user574937user574937
384
$endgroup$
$begingroup$
Is anything known about $m$ and $n$ aside from them being natural numbers?
$endgroup$
– Aleksejs Fomins
Jan 21 at 8:38
$begingroup$
@AleksejsFomins No Sir.
$endgroup$
– user574937
Jan 23 at 9:23
$begingroup$
It does not appear obvious that there is a simple closed-form function corresponding to the above sum. Why do you believe that the above sum can be found?
$endgroup$
– Aleksejs Fomins
Jan 23 at 10:03
add a comment |
0
0
0
1
$begingroup$
Find the sum $$sum_{x=1}^{m} Big(frac{2^x-1}{2^x}Big)^n$$ where $n$ belongs to natural number.
summation binomial-coefficients binomial-theorem
edited Jan 21 at 7:54
Shubham Johri
5,187717
asked Jan 21 at 7:27
user574937user574937
384
$endgroup$
Find the sum $$sum_{x=1}^{m} Big(frac{2^x-1}{2^x}Big)^n$$ where $n$ belongs to natural number.
summation binomial-coefficients binomial-theorem
summation binomial-coefficients binomial-theorem
edited Jan 21 at 7:54
Shubham Johri
5,187717
asked Jan 21 at 7:27
user574937user574937
384
edited Jan 21 at 7:54
Shubham Johri
5,187717
asked Jan 21 at 7:27
user574937user574937
384
edited Jan 21 at 7:54
Shubham Johri
5,187717
edited Jan 21 at 7:54
Shubham Johri
5,187717
edited Jan 21 at 7:54
Shubham Johri
5,187717
5,187717
asked Jan 21 at 7:27
user574937user574937
384
asked Jan 21 at 7:27
user574937user574937
384
asked Jan 21 at 7:27
user574937user574937
384
384
$begingroup$
Is anything known about $m$ and $n$ aside from them being natural numbers?
$endgroup$
– Aleksejs Fomins
Jan 21 at 8:38
$begingroup$
@AleksejsFomins No Sir.
$endgroup$
– user574937
Jan 23 at 9:23
$begingroup$
It does not appear obvious that there is a simple closed-form function corresponding to the above sum. Why do you believe that the above sum can be found?
$endgroup$
– Aleksejs Fomins
Jan 23 at 10:03
add a comment |
$begingroup$
Is anything known about $m$ and $n$ aside from them being natural numbers?
$endgroup$
– Aleksejs Fomins
Jan 21 at 8:38
$begingroup$
@AleksejsFomins No Sir.
$endgroup$
– user574937
Jan 23 at 9:23
$begingroup$
It does not appear obvious that there is a simple closed-form function corresponding to the above sum. Why do you believe that the above sum can be found?
$endgroup$
– Aleksejs Fomins
Jan 23 at 10:03
$begingroup$
Is anything known about $m$ and $n$ aside from them being natural numbers?
$endgroup$
– Aleksejs Fomins
Jan 21 at 8:38
$begingroup$
Is anything known about $m$ and $n$ aside from them being natural numbers?
$endgroup$
– Aleksejs Fomins
Jan 21 at 8:38
$begingroup$
@AleksejsFomins No Sir.
$endgroup$
– user574937
Jan 23 at 9:23
$begingroup$
@AleksejsFomins No Sir.
$endgroup$
– user574937
Jan 23 at 9:23
$begingroup$
It does not appear obvious that there is a simple closed-form function corresponding to the above sum. Why do you believe that the above sum can be found?
$endgroup$
– Aleksejs Fomins
Jan 23 at 10:03
$begingroup$
It does not appear obvious that there is a simple closed-form function corresponding to the above sum. Why do you believe that the above sum can be found?
$endgroup$
– Aleksejs Fomins
Jan 23 at 10:03
add a comment |
0
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$begingroup$
Is anything known about $m$ and $n$ aside from them being natural numbers?
$endgroup$
– Aleksejs Fomins
Jan 21 at 8:38
$begingroup$
@AleksejsFomins No Sir.
$endgroup$
– user574937
Jan 23 at 9:23
$begingroup$
It does not appear obvious that there is a simple closed-form function corresponding to the above sum. Why do you believe that the above sum can be found?
$endgroup$
– Aleksejs Fomins
Jan 23 at 10:03