n²(n+ 1)² 9. 13 + 23 + 33 +...+ n³ Vn E N. 4 1 10. 1. 2 1 + 3.4 1 1 n· (n+1) -,Vn E N n+1' 2.3 () * £ () - (";). () 11. I 2* = 3", Vn E N k k=0 k n+1 ,Vn E N, n > 1 3 12. 2 k=2 13. 3k = 4", Vn E N k...

Prove the following using mathematical induction.

Answer number 13,14, and 15 only

1 3 12. 2 k=2 13. 3k = 4", Vn E N k k=0 2 14. E 2k = 2"-1, where n is even k=0 15. I 4* = 5", Vn E N k k=0 + "/>
Extracted text: n²(n+ 1)² 9. 13 + 23 + 33 +...+ n³ Vn E N. 4 1 10. 1. 2 1 + 3.4 1 1 n· (n+1) -,Vn E N n+1' 2.3 () * £ () - (";). () 11. I 2* = 3", Vn E N k k=0 k n+1 ,Vn E N, n > 1 3 12. 2 k=2 13. 3k = 4", Vn E N k k=0 2 14. E 2k = 2"-1, where n is even k=0 15. I 4* = 5", Vn E N k k=0 +