Math & Science ⇒ New to Latex Problem with Fraction

[dynamite]

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\documentclass[11pt]{article}
\usepackage{amsmath}
%\usepackage[pdftex]{graphicx}
\usepackage{amssymb}
\usepackage{amsthm} 
\usepackage{syntonly}
%\syntaxonly
\pdfpagewidth 8.5in
\pdfpageheight 11in 
% Begin the page layout design
\setlength\topmargin{0in}
\setlength\headheight{0in}
\setlength\headsep{0in}
\setlength\textheight{7.7in}
\setlength\textwidth{6.5in}
\setlength\oddsidemargin{0in}
\setlength\evensidemargin{0in}
\setlength\parindent{0.25in}

\begin{document}
\begin{center}

\end{center}

\paragraph{(1.5)}
We attempt to prove this by induction. \\
Base Case: $n$=1 \\
$1+\frac{1}{2}=2-\frac{1}{2} \Rightarrow \frac{3}{2}=\frac{3}{2}$ This checks! \\
Inductive Case: Assume true \forall{n}: $1+\frac{1}{2} +\ldots+\frac{1}{2^n}=2-\frac{1}{2^n}$

For some reason on my inductive case, the first fraction puts everything following it under the fraction even though i only want it to be 1/2. Why is this?

[Stefan Kottwitz]

Hi,

you should have noticed errors during compilation, the math mode was not uses correctly. I've corrected one line:

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Inductive Case: Assume true $\forall{n}: 1+\frac{1}{2} +\ldots+\frac{1}{2^n}=2-\frac{1}{2^n}$

Without setting \forall{n} in math mode etc. the problem described above could occur in the output because TeX would change into math mode by itself.

Stefan

[dynamite]

Yes it is doing that.

What do you mean by math mode not used correctly and how can i fix that?

[localghost]

It seems that you are lacking some basics. A good guide through LaTeX is given with the "Unofficial LaTeX Reference Manual".


Best regards and welcome to the board
Thorsten

[Stefan Kottwitz]

What do you mean by math mode not used correctly and how can i fix that?

The math mode embedded in text can be started and ended by $, as you already know. Most symbols require the math mode, like \forall, also greek letters and other symbols, not only mathematical. Enclose complete formulas in math mode, not just variables, for instance, instead of

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Base Case: $n$=1

write

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Base Case: $n=1$

You will notice, that the second code will give a spacing around the equal sign like in the other formulas. The first code will give an improper spacing, because LaTeX cannot handle the complete formula: =1 would be set in text mode.

Btw. I would not use \\ to end a line, I would use an empty line causing a paragraph break instead of \newline.

Stefan