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Math Help - [SOLVED] Proving problem

  1. #1
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    [SOLVED] Proving problem

    \text{Given that } a_i=\frac{s}{n}+(t_i-\overline{t}), \text{where } \overline{t}=\frac{1}{n}\sum\limits_{i=1}^nt_i

    Then how do i show that:

    \sum\limits_{i=1}^na_i=s
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  2. #2
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by noob mathematician View Post
    \text{Given that } a_i=\frac{s}{n}+(t_i-\overline{t}), \text{where } \overline{t}=\frac{1}{n}\sum\limits_{i=1}^nt_i

    Then how do i show that:

    \sum\limits_{i=1}^na_i=s

     \sum_{i=1}^n(t_i-\overline{t}) =\sum_{i=1}^n(t_i)-n\overline{t}=n\overline{t}-n\overline{t}= 0

    and  \sum_{i=1}^n {s\over n}= {s\over n}\sum_{i=1}^n 1={s\over n}(1+1+1+\cdots +1)={s\over n}n=s

    Add these two and you have \sum\limits_{i=1}^na_i=s
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