SOLUTION: If 25/k = 1^2 -2^2/5 + 3^2/5^2 - 4^2/5^3+.......infinity , then what is the value of k?

Multiply through by 5



Add the two preceding sequences:











Multiply by 5



Add the two preceding sequences:





From the 2nd term on the right onward is an infinite geometric series
 with   and , so we use the formula:

         













Divide both sides by 50



Cross-multiply:



Edwin