Which of the following express 1 + 5 + 25 + 125 + 625 in sigma notation?

Question

Which of the following express 1 + 5 + 25 + 125 + 625 in sigma notation?

https://imgur.com/ToP3ON8

MULTIPLE CHOICE

II and III

I, II, and III

I and II

II only

Answer 1

This is a finite geometric series with a₁=1, r=5, n=5.

The formula for the sum of a finite geometric series is:

S_n = a₁(1-rⁿ)/(1-r).

Try substituting into the above formula to see what the result is.

Then use the definition of summation notation to determine which of the 3 choices results in the same answer.

∑⁵_k=1(5)^(k-1) = 5⁰ + 5¹ + 5² + 5³ + 5⁴ (for example).

Try the same technique for the other two choices.

Then verify here:

desmos.com/calculator/7gcdonip7o