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

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

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

We move all terms to the left:

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


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

2(T-1)+T

We add all the numbers together, and all the variables

T+2(T-1)

We multiply parentheses

T+2T-2

We add all the numbers together, and all the variables

3T-2

Back to the equation:

-(3T-2)


We get rid of parentheses

T-3T+2=0

We add all the numbers together, and all the variables

-2T+2=0

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

-2T=-2

T=-2/-2

T=1