why cant the ratio test be used on the series 1/(x^2) from x=1 to infinity?

Answer 1

Because [x→∞]lim (1/(x+1)²)/(1/x²) = [x→∞]lim x²/(x+1)² = 1. The ratio test only gives you useful information when the limit is not equal to 1.

Answer 2

because it include only one variable... ratio test is used when there is "n" and "x"... why suffer if it can be solved using nth term....