40th B.P.S.C. (Pre) 1995
Series $\sum \frac{x^2 - 2}{x^2 + 1} x^2, x < 0$
aConvergent for $x \ge 1$
bConvergent for $x = 1$
cDivergent for $x \ge 1$✓ Correct
dDivergent for $x ? 1$
Explanation
From CR. Test $x^2 \ne 0$ $\lim_{n \to 0} \left( \frac{n^2 - 1}{n^2 + 1} x \right)^{\frac{1}{n}}$ While $x > 0$ $x \ge 1$ So, it is divergent for $x \ge 1$
general-mental-ability