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

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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

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