Solve 1/pi[-1^n/n^2+-1/n^2]

$$\frac { 1 } { \pi } [ \frac { - 1 ^ { n } } { n ^ { 2 } } + \frac { - 1 } { n ^ { 2 } } ]$$

Evaluate

$$-\frac{2}{\pi n^{2}}$$

Short Solution Steps

Since \frac{-1^{n}}{n^{2}} and \frac{-1}{n^{2}} have the same denominator, add them by adding their numerators.

$$\frac{1}{\pi }\times \frac{-1^{n}-1}{n^{2}}$$

Combine like terms in -1^{n}-1.

$$\frac{1}{\pi }\times \frac{-2}{n^{2}}$$

Multiply \frac{1}{\pi } times \frac{-2}{n^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2}{\pi n^{2}}$$

Differentiate w.r.t. n

$$\frac{4}{\pi n^{3}}$$