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#### ATroelstein

##### New member

- Jun 30, 2012

- 15

$$T(n)=aT(n-1)+bn$$

Using substitution, I have solved it to the following form

$$T(n)=a^{n-1}+b \sum_{i=2}^{n}ia^{n-i}$$

Now I am trying to prove my solution is correct using induction, but I'm a bit lost. Any advice on how to conduct this proof would be appreciated. Thank you.