4. Show that if k is a triangular number, then 8k + 1 is a perfect square. 5. A pentagonal pyramidal number P, can be determined using the dot representations of pentagonal number, the same way with...

Extracted text: 4. Show that if k is a triangular number, then 8k + 1 is a perfect square. 5. A pentagonal pyramidal number P, can be determined using the dot representations of pentagonal number, the same way with the triangular and square pyramidal numbers. Determine the first five pentagonal pyramidal numbers. () 1 6. If C, is the nth Catalan number, then C, can be expressed as C, = Show that n+1 (:) („".) 2n a. C, = (2n + : ь. С, 2n + 1