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Jul
27
comment Algebraic proof that $\sum\limits_{i=0}^n \binom{i}{k} = \binom{n + 1}{k + 1}$
Hint: This is the pascal's triangle column-sum property. Try to use induction.
Jul
8
revised Database of unsolved problems in mathematics
Corrected spelling
Jul
8
comment Database of unsolved problems in mathematics
This is one of may sources: unsolveddatabase.org/about
Jul
8
suggested approved edit on Database of unsolved problems in mathematics
Jul
8
comment Solve the determinant.
At least present what the determinant calculation you have made.
Jul
7
comment How do I evaluate this:$\sum_{n=1}^{\infty}\frac{1}{n²}(e^x −1 −\frac{x}{1!} −\frac{x²}{2!}−\cdots\frac{x^n}{n!})$?
Using Maclaurin Expansion: $$-e^x=\sum_{n=0}^{\infty}( −1 −\frac{x}{1!} −\frac{x²}{2!}−\cdots\frac{x^n}{n!})$$
Jul
7
revised Find function satisfying specific conditions
Changed title to match question text
Jul
7
suggested approved edit on Find function satisfying specific conditions
Jul
7
comment Find function satisfying specific conditions
very clever indeed
Jul
4
comment What is the maximum amount of solutions to $f(x+1)f(x)= ax^2+bx+c$.
Since the expression:$g(x)=f(x)f(x+1) - (ax^2+bx+c$) is a 2nd degree polynomial, you can't get more than 2 solutions (assuming m and h are not function of x).
Jul
4
comment Original price formula after discount
Yes your answer is correct.
Jul
1
comment Explain why two right triangles, each with an acute angle of 17 degrees, must be similar.
Study the properties of "Similar Triangles" as in mathopenref.com/similartriangles.html for example.
Jul
1
comment Use the graph of Y=f(x) shown below to answer the following questions
Good explanation. I appreciate it.
Jul
1
comment Use the graph of Y=f(x) shown below to answer the following questions
I assumed that since x=1 and x=3 are roots, then the function must be (x-1)(x-3) but apparently there is more than 1 second degree polynomial that has the same roots! Thanks for the explanation. It would be nice to know how to generate all such polynomials that share the same roots then...I feel something is not quite right but it is 2 A.M. and I am not thinking straight.
Jun
30
comment Use the graph of Y=f(x) shown below to answer the following questions
f(0) = 1.5, so f(x) is not equal (x-1)(x-3) as you suggested.
Jun
30
comment Use the graph of Y=f(x) shown below to answer the following questions
Are you allowed to find values such as f(2) directly from the curve?
Jun
30
revised Use the graph of Y=f(x) shown below to answer the following questions
Copied some of the text in the picture into the question body to make reading it easier
Jun
30
suggested approved edit on Use the graph of Y=f(x) shown below to answer the following questions
Jun
30
comment Number of combinations where the sum of values must be the same
If you were looking for integer values for $a_i$, then the concept of "Integer Partitioning" would apply. However with $a_i$<1, I don't think there would be a closed form for the different number of ways.
Jun
30
answered Using induction to study the sequence $\sqrt{6} , \sqrt{6 +\sqrt{6}}, \dots$