# Evaluate sum from n=2 to 10 of 25(0.3)^(n+1)

Split the summation to make the starting value of equal to .
Evaluate .
Factor out of the summation.
Use the exponentiation to adjust the lower and upper bounds.
Lower bound:
Upper bound:
Rewrite the geometric summation with the new bounds.
Split the summation to make the starting value of equal to .
Evaluate .
The formula for the geometric series is:
Substitute the values into the formula.
Simplify.
Simplify the numerator.
Raise to the power of .
Multiply by .
Subtract from .
Simplify the expression.
Subtract from .
Divide by .
Evaluate .
Expand the series for each value of .
Simplify.
Simplify each term.
Subtract from .
Anything raised to is .
Subtract from .
Evaluate the exponent.
Replace the summations with the values found.
Simplify.
Subtract from .
Multiply by .
Evaluate .
Expand the series for each value of .
Simplify.