Evaluate the Summation sum from i=1 to 8 of 0.8^i

Problem

(∑_i=1^8)(0.8)

Solution

1. Identify the type of series. This is a finite geometric series where the first term a is 0.8=0.8 the common ratio r is 0.8 and the number of terms n is 8

2. Apply the formula for the sum of a finite geometric series, which is (S_n)=(a*(1−rn))/(1−r)

3. Substitute the values a=0.8 r=0.8 and n=8 into the formula.

(S_8)=(0.8*(1−0.8))/(1−0.8)

4. Simplify the denominator.

(S_8)=(0.8*(1−0.8))/0.2

5. Divide the coefficients.

(S_8)=4*(1−0.8)

6. Calculate the numerical value.

0.8=0.16777216

(S_8)=4*(1−0.16777216)

(S_8)=4*(0.83222784)

(S_8)=3.32891136

Final Answer

(∑_i=1^8)(0.8)=3.32891136

Want more problems? Check here!