11. Let n be an integer, 
![[n]](https://s0.wp.com/latex.php?latex=%5Bn%5D&bg=ffffff&fg=111111&s=0 "[n]")
12. Prove by mathematical induction that 
13. Show that the number of distinct ways of triangulating a convex n-gon by 
14. Show that the number of solutions of the equation 
15. Show that for each n and k, 
16. Calculate
![\sum_{A \subseteq [n]}|A|^{2}](https://s0.wp.com/latex.php?latex=%5Csum_%7BA+%5Csubseteq+%5Bn%5D%7D%7CA%7C%5E%7B2%7D&bg=ffffff&fg=111111&s=0 "\sum_{A \subseteq [n]}|A|^{2}")
17. Calculate ![\lim_{n \rightarrow \infty} \sqrt[n]{\sum_{k=0}^{n} {n \choose k}^{t}}](https://s0.wp.com/latex.php?latex=%5Clim_%7Bn+%5Crightarrow+%5Cinfty%7D+%5Csqrt%5Bn%5D%7B%5Csum_%7Bk%3D0%7D%5E%7Bn%7D+%7Bn+%5Cchoose+k%7D%5E%7Bt%7D%7D&bg=ffffff&fg=111111&s=0 "\lim_{n \rightarrow \infty} \sqrt[n]{\sum_{k=0}^{n} {n \choose k}^{t}}")
18. Let k be a non-negative integer number. Show that any non-negative integer number n can be written uniquely as
19. Let 
20. Determine the number of ways of writing a positive integer n as a sum of ones and twos.
More later,
Nalin Pithwa
