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**BIOS** $\displaystyle (0 + 1 + 2 .... + k + k + 1) = \frac{(k+1)((k+1) + 1)}{2}$

Using induction Hypothesis that P(k) holds, the left side can be rewritten:

$\displaystyle \frac{k(k+1)}{2} +(k+1)$

It's the next part I don't get:

Algebraically:

$\displaystyle \color{blue}\frac{k(k+1)}{2} +(k+1) = \frac{k(k+1)+2(k+1)}{2}$

$\displaystyle \color{blue}\frac{k(k+1)}{2} +(k+1) = \frac{(k+1)(k+2)}{2}$

$\displaystyle \frac{k(k+1)}{2} +(k+1) = \frac{(k+1)((k+1) + 1)}{2}$

Where are the first two expressions coming from on the right hand side here? :?