Question

How would you write sn = 1 + a + a² + ... + aⁿ in summation notation?

A. ∑ k=0 to n aᵏ.
B. ∑ k=1 to n aᵏ.
C. ∑ k=0 to n+1 aᵏ.
D. ∑ k=1 to n+1 aᵏ.

Answer 1

The expression sn = 1 + a + a² + ... + aⁿ can be written as ∑ k=0 to n aᵏ in summation notation.

Step-by-step explanation:

The expression sn = 1 + a + a² + ... + aⁿ can be written in summation notation as ∑ k=0 to n aᵏ.

In this notation, the variable k represents the index of summation, which starts at 0 and goes up to n. The term aᵏ represents each term in the sequence where a is the common ratio and k is the exponent of a.

For example, if a = 2 and n = 3, the summation notation ∑ k=0 to 3 2ᵏ would represent the sequence 1 + 2 + 4 + 8 = 15.