In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 2+2^2+2^3+⋯+ 2^11

Key Concepts

Summation Notation

Summation notation is a mathematical shorthand used to represent the sum of a sequence of terms. It typically uses the Greek letter sigma (Σ) to denote the sum, with limits indicating the starting and ending indices. For example, Σ from i=1 to n of a_i represents the sum of the terms a_1, a_2, ..., a_n.

Exponential Functions

Exponential functions are mathematical functions of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent. In the context of the given question, the terms 2^1, 2^2, ..., 2^11 represent an exponential sequence where the base is 2, and the exponent increases incrementally.

Index of Summation

The index of summation is a variable used to represent the position of terms in a sequence being summed. In this case, 'i' serves as the index, starting from 1 and increasing by 1 for each term until it reaches 11. This allows for a concise representation of the sum of terms in a series.