Let a n = 16 , 4 , 1 , … … be a geometric sequence. The value of ∑ n = 1 ∞ P n n , where P n is the product of the first n terms, is equal to.

Step-by-step solution

For the G.P. a , a r , a r 2 , … … … P n = a a r a r 2 … . . a r n - 1 = a n r n n - 1 2 ⇒ P n n = a r n - 1 2 ⇒ ∑ n = 1 ∞ P n n = a 1 + r + r + r r + . … … = a 1 - r Given, a = 16 and r = 1 4 = 16 1 - 1 4 = 32