# Tagged Questions

39 views

### The sum of palindromes from 100 to 900

I'm working with palindromes from $100-999$. I'm having trouble with the step highlighted in red. Can someone explain the algebra to me? Taken from: Discrete and Combinatorial Mathematics: An ...
52 views

39 views

### Prove that maximum 9 trailing zeroes in this summation

I am trying to prove that there are a maximum of 9 trailing $0$'s at the end of this summation: $$\sum_{k=1}^{k=m} k^n$$ for $1\le n\le 1000000$ and $m\le 100$. Any help on how to approach?
125 views

### Recurrence Relation Solving Problem

Can anyone help me in solving this complex recurrence in detail? $T(n)=n + \sum\limits_{k-1}^n [T(n-k)+T(k)]$ $T(1) = 1$. We want to calculate order of T. I'm confused by using recursion tree ...
97 views

19 views

### Proving claims about sequences by induction?

I am learning how to prove claims about finite sequences right now. Can you help me prove or disprove the following claim? ...
18 views

66 views

### Proving for all n that $\sum_{i=0}^n \frac1{2^{i}} < 2$

Proving for all n $\in \mathbb N$, $$\sum_{i=0}^n \frac1{2^{i}} < 2$$ Hint. First prove that the left hand side can be expressed in closed form, i.e. without using the summation operator. This is ...
9 views

### Proving a disequality involving hypergeometric distribution

How would you prove symbolically the following property? $$H(m_a+1,p_a+1,m,p) < H(m_a,p_a,m,p)$$ where $H(m_a,p_a,m,p)$ is the probability of drawing $m_a$ white balls in a series of $m$ ...
25 views

94 views

### Derive Closed form sum of N^2

Can anyone explain to me how you would derive this ? I have this question asked in a CS class and can't figure out how to derive it. it has to be derived as you would with sum of N ex ...
61 views

### Exponentiation in terms of Summation

For positive integers, $a \times b=\sum\limits^{b}{a}$, correct? So therefore exponentiation where n is also a positive integer should be something like $a^n=\sum\limits^n{\sum\limits^a{a}}$ This is ...
149 views

### Calculating $\displaystyle\sum_{i=1}^{n} \binom{i}{2}$

Show $\displaystyle\sum_{i=1}^{n} \binom{i}{2}=\binom{n+1}{3}$. I'm thinking right now (though not getting anywhere with it) that I want to expand out the summation portion to $i!/2!(i-2)!$ and ...
### How to show that $\sum\limits_{k=0}^{\lfloor0.999n\rfloor}\binom{2n}{k} < \binom{2n}{n}$ holds for large n
It seems logical to me since $\binom{2n}{n}$ is in the middle of the row in pascal triangle; therefore, the largest, and for large n the sum adds only the small ones on the left. But I do not have any ...