T(n)=T(n-1)+2n

Solution for T(n)=T(n-1)+2n equation:

(T)=(T-1)+2T

We move all terms to the left:

(T)-((T-1)+2T)=0


We calculate terms in parentheses: -((T-1)+2T), so:

(T-1)+2T

We add all the numbers together, and all the variables

2T+(T-1)

We get rid of parentheses

2T+T-1

We add all the numbers together, and all the variables

3T-1

Back to the equation:

-(3T-1)


We get rid of parentheses

T-3T+1=0

We add all the numbers together, and all the variables

-2T+1=0

We move all terms containing T to the left, all other terms to the right

-2T=-1

T=-1/-2

T=1/2