Solve s(n)=5/n^2[n(n+1)/2]

$$s ( n ) = \frac { 5 } { n ^ { 2 } } [ \frac { n ( n + 1 ) } { 2 } ]$$

Evaluate

$$\frac{5}{2}+\frac{5}{2n}$$

Short Solution Steps

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

$$\frac{5}{n^{2}}\times \frac{n^{2}+n}{2}$$

Multiply \frac{5}{n^{2}} times \frac{n^{2}+n}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(n^{2}+n\right)}{n^{2}\times 2}$$

Factor the expressions that are not already factored.

$$\frac{5n\left(n+1\right)}{2n^{2}}$$

Cancel out n in both numerator and denominator.

$$\frac{5\left(n+1\right)}{2n}$$

Expand the expression.

$$\frac{5n+5}{2n}$$

Expand

$$\frac{5}{2}+\frac{5}{2n}$$

Short Solution Steps

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

$$\frac{5}{n^{2}}\times \frac{n^{2}+n}{2}$$

Multiply \frac{5}{n^{2}} times \frac{n^{2}+n}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(n^{2}+n\right)}{n^{2}\times 2}$$

Factor the expressions that are not already factored.

$$\frac{5n\left(n+1\right)}{2n^{2}}$$

Cancel out n in both numerator and denominator.

$$\frac{5\left(n+1\right)}{2n}$$

Expand the expression.

$$\frac{5n+5}{2n}$$