Hi guys i am trying to solve the following theorem

Theorem :If $\displaystyle X_1,X_2,...X_n$ constitute the random sample from an infinite population with the mean $\displaystyle \mu$ and variance $\displaystyle \sigma^2$, then

$\displaystyle E[\bar X] = \mu$ and $\displaystyle var(\bar X) = \frac{\sigma^2}{n}$

Solution:Let $\displaystyle Y = \bar X$

$\displaystyle Y = \sum a_i \ X_i$

$\displaystyle \therefore $ $\displaystyle E[\bar X] = E \left( \sum a_i \ X_i \right)$

Let $\displaystyle a_i = \frac{1}{n}$ and as $\displaystyle E[\bar X] = \mu$ therefore substituting these terms in the above equation we get

$\displaystyle E[\bar X] = \sum_{n=1}^{\infty} \frac{1}{n} \mu$

Now after this in the book it shows this step

$\displaystyle \sum_{n=1}^{\infty} \frac{1}{n} \mu$ = $\displaystyle n. \frac{1}{n} \mu$...............How did he get 'n' instead of $\displaystyle \sum_{n=1}^{\infty}$