1. [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:

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

2. Originally Posted by noob mathematician
$\text{Given that } a_i=\frac{s}{n}+(t_i-\overline{t}), \text{where } \overline{t}=\frac{1}{n}\sum\limits_{i=1}^nt_i$

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