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## Main Question or Discussion Point

I am familiar with the proof for the following variant of the triangle inequality:

|x+y| ≤ |x|+|y|

However, I do not understand the process of proving that there is an equivalent inequality for an arbitrary number of terms, in the following fashion:

|x_1+x_2+...+x_n| ≤ |x_1|+|x_2|+...+|x_n|

How do I prove this? Please write down the solution step by step. I know that the Cauchy-Schwartz inequality is used for proving this in the case where n=2, but is it possible to use it for any n?

Thank you,

Dobedobedo!

|x+y| ≤ |x|+|y|

However, I do not understand the process of proving that there is an equivalent inequality for an arbitrary number of terms, in the following fashion:

|x_1+x_2+...+x_n| ≤ |x_1|+|x_2|+...+|x_n|

How do I prove this? Please write down the solution step by step. I know that the Cauchy-Schwartz inequality is used for proving this in the case where n=2, but is it possible to use it for any n?

Thank you,

Dobedobedo!