Hi, I understand the sequence of the example I am working through, but I cannot understand some of the "simplification" (i.e. when one expression is simplified to mean the same thing)

The example is

Prove inductively for all integers n >= 1,

1+2+3....+n = $\displaystyle n(n+1) / 2$ ---> *

i) i understand s(subscript m ??) is true, I prove this by substituting an integer for n

ii) sn+1 is true when n>=m and sn are true

To prove for Sk+1 is true for n = k+1;

original k(k+1)/2 becomes

k(k+1)/2 + (k+1) ---I understand this is proof for n=k+1 where n is the formula above, marked ---> *

but I do not understand the next step in the example, where

(a) k(k+1)/2 + (k+1) <---this formula is simplified to:

= (b) (k+1)(k+2) / 2 <--- I don't understand how they went from (a) to (b) here.

I thought

k(k+1)/2 + (k+1) = k squared + k / 2 + (k+1) (sorry I can't get super/sub script to work)

Thanks for any help, sorry if my explanation seems jumbled or unreadable(if so I will try to post the example again more clearly)