Solve 1994/n^3(n(n+1)/2)

$$\frac { 1994 } { n ^ { 3 } } ( \frac { n ( n + 1 ) } { 2 } )$$

Evaluate

$$\frac{997\left(n+1\right)}{n^{2}}$$

Short Solution Steps

Use the distributive property to multiply n by n+1.

$$\frac{1994}{n^{3}}\times \frac{n^{2}+n}{2}$$

Multiply \frac{1994}{n^{3}} times \frac{n^{2}+n}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1994\left(n^{2}+n\right)}{n^{3}\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{997\left(n^{2}+n\right)}{n^{3}}$$

Factor the expressions that are not already factored.

$$\frac{997n\left(n+1\right)}{n^{3}}$$

Cancel out n in both numerator and denominator.

$$\frac{997\left(n+1\right)}{n^{2}}$$

Expand the expression.

$$\frac{997n+997}{n^{2}}$$

Expand

$$\frac{997\left(n+1\right)}{n^{2}}$$

Short Solution Steps

Use the distributive property to multiply n by n+1.

$$\frac{1994}{n^{3}}\times \frac{n^{2}+n}{2}$$

Multiply \frac{1994}{n^{3}} times \frac{n^{2}+n}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1994\left(n^{2}+n\right)}{n^{3}\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{997\left(n^{2}+n\right)}{n^{3}}$$

Factor the expressions that are not already factored.

$$\frac{997n\left(n+1\right)}{n^{3}}$$

Cancel out n in both numerator and denominator.

$$\frac{997\left(n+1\right)}{n^{2}}$$

Expand the expression.

$$\frac{997n+997}{n^{2}}$$