Answer by Bill Dubuque for Arithmetic summation question - I don't understand...
$\begin{eqnarray}{\bf Hint}\quad f_1 + \cdots + f_n &=&\, -f_0 + (\color{#c00}{f_0\! +\cdots +\! f_{n-1}}) + \color{#0a0}{f_n}\\ \\ &=&\quad 0 \,\ +\ \color{#c00}{\dfrac{n(n\!-\!1)}2}\...
View ArticleAnswer by Ross Millikan for Arithmetic summation question - I don't...
You have $$\sum_{i=1}^n=\frac 12n(n+1)$$ If you don't like the substitution given by Brian M. Smith, you can just make the correction: $$\sum_{i=0}^{n-1}i=\sum_{i=1}^n=\frac 12n(n+1)-n=\frac 12n(n-1)$$...
View ArticleAnswer by Jorge for Arithmetic summation question - I don't understand this...
$2(1+2+3+4+5...+n)=(1+2+3...+n)+(n+(n-1)+....+2...+1)$. Now add the first one in the first bracket with the first one of the second bracket, the second of the first with the second of the second and so...
View ArticleAnswer by Brian M. Scott for Arithmetic summation question - I don't...
It’s really just a substitution. You have the formula $$\sum_{i=1}^ni=\frac{n(n+1)}2\;.\tag{1}$$ Suppose that $n=m-1$; then $(1)$...
View ArticleArithmetic 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 understand...
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