Summation using binomial theorem
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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
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add a comment |
$begingroup$
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
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Is anything known about $m$ and $n$ aside from them being natural numbers?
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– Aleksejs Fomins
Jan 21 at 8:38
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@AleksejsFomins No Sir.
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– user574937
Jan 23 at 9:23
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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?
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– Aleksejs Fomins
Jan 23 at 10:03
add a comment |
$begingroup$
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
$endgroup$
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
5,187717
asked Jan 21 at 7:27
user574937user574937
384
384
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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 |
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ReI,sM DQh7R CK6,U,ch0TYeiy,msZz6 TRfDWQxHGqO 3ywGm7pvU WJQrDtCVl04
$begingroup$
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