Question

What is the sum of ∞Σn=1 2(1/5)^n-1? s=1/5 s=2/5 s=5/3 s=5/2

Answer 1

The sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2

How to determine the sum of the notation?

The sum notation is given as:

∞Σn=1 2(1/5)^n-1

The above notation is a geometric sequence with the following parameters

• Initial value, a = 2
• Common ratio, r = 1/5

The sum is then calculated as

S = a/(1 - r)

The equation becomes

S = 2/(1 - 1/5)

Evaluate the difference

S = 2/(4/5)

Express the equation as products

S = 2 * 5/4

Solve the expression

S= 5/2

Hence, the sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2

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