Solve 1-e^{-(2n+1)pi}

Evaluate

1 - e^{- (2 n + 1) π}

To find the roots of the expression,set the expression equal to 0

1 - e^{- (2 n + 1) π} = 0

Multiply the terms

1 - e^{- π (2 n + 1)} = 0

Move the constant to the right-hand side and change its sign

- e^{- π (2 n + 1)} = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

- e^{- π (2 n + 1)} = - 1

Change the signs on both sides of the equation

e^{- π (2 n + 1)} = 1

Write the number in exponential form with the base of e

e^{- π (2 n + 1)} = e^{0}

Since the bases are the same,set the exponents equal

- π (2 n + 1) = 0

Change the sign

π (2 n + 1) = 0

Rewrite the expression

2 n + 1 = 0

Move the constant to the right side

2 n = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

2 n = - 1

Divide both sides

\frac{2 n}{2} = \frac{- 1}{2}

Divide the numbers

n = \frac{- 1}{2}

Solution

n = - \frac{1}{2}

Alternative Form

n = - 0.5

1 E^{ (2n+1)pi}