Evaluate 1+1/2+1/4+1/8+1/16+1/32+1/64

Problem

1+1/2+1/4+1/8+1/16+1/32+1/64

Solution

1. Identify the expression as a finite geometric series where the first term a=1 and the common ratio r=1/2

2. Count the number of terms in the sum, which is n=7

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

4. Substitute the values into the formula:

(S_7)=(1*(1−(1/2)7))/(1−1/2)

5. Simplify the numerator and denominator:

(S_7)=(1−1/128)/1/2

6. Calculate the final value by multiplying the numerator by the reciprocal of the denominator:

(S_7)=127/128⋅2

(S_7)=127/64

Final Answer

1+1/2+1/4+1/8+1/16+1/32+1/64=127/64

Want more problems? Check here!