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Answer each of the following. You will upload a file containing your answers to both of these questions. You may hand write and scan, if desired. Please ensure the writing is clear and easy to read. a) Use mathematical induction to prove that:

`\sum_(i=1)^n (i(i+1))/(2)=(n(n+1)(n+2))/(6)`

b) Solve the following recurrence relation to a closed form solution using whichever technique you prefer.

```
T(1)=2
T(n)=2T(n-1)+n2^(n), for n>1
```