Consider the statement P(n) : 2n + 1 < 2n. Since P(3) is true, we assume by mathematical induction that k >= 3 and P(k) is true so that 2(k + 1) + 1 = 2k + 2 + 1 < 2k + 2 < 2k + 2k = 2k + 1. Can you explain each algebraic step of the last long expression clearly? I understand the concept of induction, I just need help with the algebra. Thanks!
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
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Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
Consider the statement P(n) : 2n + 1 < 2n. Since P(3) is true, we assume by mathematical induction that k >= 3 and P(k) is true so that 2(k + 1) + 1 = 2k + 2 + 1 < 2k + 2 < 2k + 2k = 2k + 1. Can you explain each algebraic step of the last long expression clearly? I understand the concept of induction, I just need help with the algebra. Thanks!
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