CSC 344 - Algorithms and Complexity

Dr R. M. Siegfried

Assignment #1 - Some basic mathematical induction practice

Due Friday, January 27, 2017

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1. Prove by mathematical induction that $\sum _{i=1}^n{i}^2=\frac{n(n+1)(2n+1)}{6}$
2. Prove by mathematical induction that $\sum _{i=1}^n{i}^3=\frac{n^2{(n+1)}^2}{4}$
3. Prove by mathematical induction that $\sum _{i=1}^n\frac{1}{2^i}=1-\frac{1}{2^n}$
4. Prove by mathematical induction that $\sum _{i=1}^n{a}^i\le \frac{a^{n+1}-1}{a-1}$
5. Prove by mathematical induction that $\sum _{i=1}^n{2}^i\le 2^{n+1}-1$

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