Solve T(n)=5T(n/4)+n

$$T ( n ) = 5 T ( \frac { n } { 4 } ) + n$$

Evaluate

$$\frac{5Tn}{4}+n$$

Solution Steps

Express 5\times \frac{n}{4} as a single fraction.

$$\frac{5n}{4}T+n$$

Express \frac{5n}{4}T as a single fraction.

$$\frac{5nT}{4}+n$$

To add or subtract expressions, expand them to make their denominators the same. Multiply n times \frac{4}{4}.

$$\frac{5nT}{4}+\frac{4n}{4}$$

Since \frac{5nT}{4} and \frac{4n}{4} have the same denominator, add them by adding their numerators.

$$\frac{5nT+4n}{4}$$

Factor

$$\frac{n\left(5T+4\right)}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{5Tn+4n}{4}$$

Consider 5Tn+4n. Factor out n.

$$n\left(5T+4\right)$$

Rewrite the complete factored expression.

$$\frac{n\left(5T+4\right)}{4}$$