Tagged Questions

2answers
75 views

The sum of $1^2+7^2+13^2+\cdots+n^2,$ where $n =1 \mod6$

Find the sum of this progression in the terms of $n$ $$1^2+7^2+13^2+\cdots+n^2,$$ where $n =1 \mod6$. Are Bernoulli's numbers involved in this? Please help.
0answers
104 views

Evaluate this product $n \times \frac{n-1}{2} \times \dots \times \frac{n-(2^k-1)}{2^k}$

For $k = \lfloor \log_{2}(n+1) \rfloor - 1$ evaluate $n \times \frac{n-1}{2} \times\frac{n-3}{4} \times \frac{n-7}{8} \times \dots \times \frac{n-(2^{k}-1)}{2^k}$ So the product goes up to $k$ and I ...
2answers
344 views

n more each day

It's been a while since I've been at school and I don't work in a field that practices this sort of stuff so I don't know the formula my brain can't wrap my head around the problem. The problem: You ...
1answer
65 views

Rewrite and approximate the sum as an Integral $\sum_{i=1}^{1000} \sqrt{i}$ [closed]

This is not an Infinite sum !, how do we change this to an Integral.  We normally write an integral as an infinite sum.
1answer
116 views

6answers
61 views

Why does $1+2+3+…+p = {(1⁄2)}\cdotp\cdot(p+1)$ [duplicate]

I saw this from Project Euler, problem #1: If we now also note that $1+2+3+...+p = {(1/2)} \cdot p\cdot(p+1)$ What is the intuitive explanation for this? How would I go about deriving the latter ...
3answers
42 views

0answers
29 views

How does one change the top number in a summation?

Sorry I do not know the correct term (I am guessing "upper limit"). Here is what I mean. $$\sum\limits_{i=1}^{\color{red}{17}}\frac{2i}{i+3}$$ The $17$ is what I am talking about as "the top number". ...
3answers
46 views

Evaluating $\sum_{k=1}^{30} k(30-k)$

I tried to rewrite it as $\sum_{k=1}^{30} k(30-\sum_{k=1}^{30}k)$ and then replace the $\sum_{k=1}^{30} k$ with $\frac{n(n+1)}{2}$ then substitute $n=30$ into the equation, however I am not getting ...
1answer
18 views

2answers
114 views

Sequential sums $1+2+\cdots+N$ that are squares [duplicate]

While playing with sums $S_n = 1+\cdots+n$ of integers, I have just come across some "mathematical magic" I have no explanation and no proof for. Maybe you can give me some comments on this: I had ...
4answers
84 views

Arithmetic summation question - I don't understand this answer.

I'm really sorry for this basic, stupid question. I have been looking for answers online but I can't find any. I don't understand the following summation: $$\sum_{i=0}^{n-1}i=\frac{n(n-1)}2$$ I ...
2answers
33 views

Is this possible?

Is it possible to convert this forumla $$r(\theta) = \sum_{n=0}^\theta\left(\frac{2n+1}{2}\right)$$ to one without the $\sum$ sign? If so, how?
2answers
88 views

How can I compute this sum of binomial

Is there any way to compute the following sum: $\displaystyle{ \sum_{\ell = {n + 1 \over{\vphantom{\LARGE A}2}}}^{n}{n \choose \ell}5^{n - \ell}}$ where $n$ is odd. Thank you.
0answers
65 views