+0  
 
0
216
1
avatar

Consider the geometric series 4 + 20/a + 100/a^2 + .... If the sum is a perfect square, what is the smallest possible value of a where is a positive integer?

 Jun 27, 2022
 #1
avatar+128079 
+1

The common  ratio  =  5/a

 

The  sum  =          4 / ( 1 -5/a)  =  (4)  /  [ ( a - 5) / a ] =     (4a) / (a - 5)

 

The smallest integer value of  a  that produces a perfect square is when   a =   9

 

 

cool cool cool  

 Jun 27, 2022

5 Online Users

avatar
avatar
avatar
avatar