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comment Weird Induction…?
your second formula is apparerently wong: it says that $\binom{n + k + 1}{k}$ is constant, independent of $k$. So check your formula, you made an error. It is $$\sum_{i = 0}^{k} \binom{n + i}{i} = \binom{n + k + 1}{k}$$ for $0 \leq k \leq n$
Jul
16
comment Calculate 2000! (mod 2003)
Of course you have to prove that 2003 is a prime otherwise you can't be sure that the result is true.
Jul
10
comment Interchanging order of summation mechanically
"No thinking required here, just algebra" is not true. Actually your result is ok. But if you dont know if the rules that you apply are allowed, you dont know if the result is true. Simply doing some algebra on parts of yor graphic (your summation formula) does not guarantee a correct result
Jul
10
comment Interchanging order of summation mechanically
you are interchanging two lim operation. Can you tell me why this is allowed here?
Jul
10
comment Interchanging order of summation mechanically
The $i$ in your first and second formula does not make sense to me. Is this a constant?
Jul
8
comment Set theory formula
Tjis may be a useful advice for the OP but it is not an answer to the question.
Jul
6
comment Squaring both sides of an inequality: attempt to prove a general rule
@AlexanderVigodner; I can't see any difference between your proof and the proof of the OP excep that the OP's proof is more wordy. Or do I miss something?
Jul
6
comment What does it even mean to say 'preserve structure'?
source:me seems not to be a valid URL
Jul
6
comment What does it even mean to say 'preserve structure'?
if you cite another source it woul be fine if you provide a link to the source.
Jul
4
comment Are there numbers such that A + B = 10A+B?
Did you asked which two 2-digit numbers AB and CD sum up to a 4-digit number ABCD in the first title of you question?
Jul
4
comment Solving an equation that contains a logarithm
I was not satisfied with the formulation of the problem. My English is not very good, but I think 'express' is an appropriate term . If it not, please ´help tofind the right word.
Jul
4
comment Resultant Temperature
14*m_1 + 38*m_3 = 28*(m_1 + m_3) means that the resultant temperature is 28C if the temperature of the first liquid was 14C and the third was 38C. The calculation is right but you answered another question.
Jul
1
comment Defining exponentiation on the integers
@Cameron Buie: yes, I forgot them. Thx
Jul
1
comment Defining exponentiation on the integers
of course you could. use the biomial theorem.
Jun
30
comment Logic problem involving sum of digits
@Mike: you are right, but I mentioned that one can construct other solutions by adding/removing zeros
Jun
30
comment Complex numbers $z$ satisfying $|z−a|+|z+a| = 2|b|\Leftrightarrow |a|\le |b|$.
If you draw the complex numbers as points in the plane your equation describes what kind of figure?
Jun
30
comment Complex numbers $z$ satisfying $|z−a|+|z+a| = 2|b|\Leftrightarrow |a|\le |b|$.
What is the first implication and what is the second one? Please show us the prove.
Jun
30
comment Are 7 and 49 coprime?
@Ben: better than "Thanks": accept the answer.
Jun
30
comment Logic problem involving sum of digits
$11101110111^2=123234645696546432321$ is another one
Jun
30
comment Logic problem involving sum of digits
@Donkey Kong: No, $S(n^2)$ means squaring the number $n$ and then taking the sum of digit.