# Science:Math Exam Resources/Courses/MATH220/April 2005/Question 05

MATH220 April 2005

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Other MATH220 Exams

### Question 05

Let ${\displaystyle a_{1},a_{2},a_{3},\ldots }$ be real numbers. Prove, using induction, that for all ${\displaystyle n\in \mathbb {N} }$,

${\displaystyle \left|\sum _{k=1}^{n}a_{k}\right|\leq \sum _{k=1}^{n}|a_{k}|}$

You may assume the Triangle Inequality in the form

${\displaystyle |x+y|\leq |x|+|y|}$

for all real numbers x and y.

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