Suppose thatx1,x2,x3, ... ,xnare real numbers. Prove (using mathematical induction) that

lx1 +x2 + ... +xnl<lx1l + lx2l + ... + lxnl

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- Feb 10th 2009, 09:24 AMbearej50Mathematical Induction
Suppose that

*x*1,*x*2,*x*3, ... ,*xn*are real numbers. Prove (using mathematical induction) that

l*x*1 +*x*2 + ... +*xn*l__<__l*x*1l + l*x*2l + ... + l*xn*l - Feb 10th 2009, 04:41 PMThePerfectHacker
- Feb 16th 2009, 10:12 AMbearej50
http://www.mathhelpforum.com/math-he...728e1577-1.gif

I know this to be true. I can use this theorem in my proof. I just dont know how to write a proof for this using mathematical induction. - Feb 16th 2009, 10:26 AMThePerfectHacker
You will prove this for $\displaystyle n\geq 2$. If this statement is true for $\displaystyle k$ variables i.e. $\displaystyle |x_1+...+x_k| \leq |x_1| + ... + |x_k|$ we shall prove it is true for $\displaystyle k+1$ variables. In the expression $\displaystyle |x_1+...+x_k+x_{k+1}|$ think of it as $\displaystyle |(x_1+...+x_k)+x_{k+1}|$ but this is less than or equal to $\displaystyle |x_1+...+x_k| + |x_{k+1}|$ but this is less than or equal to $\displaystyle |x_1|+...+|x_k|+|x_{k+1}|$.

- Feb 17th 2009, 11:30 AMbearej50
thank you again