Proof by deduction | IB Math AAHL | Perplex

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Topics

Exponents & Logarithms Rounding & Error Sequences & Series Counting & Binomials Proof and Reasoning Complex Numbers Algebra Skills

Cartesian plane & lines Quadratics Function Theory Transformations & asymptotes Polynomials

2D & 3D Geometry Trig equations & identities Vectors

Probability Descriptive Statistics Bivariate Statistics Distributions & Random Variables

Differentiation Integration Differential Equations Maclaurin

Review Videos Formula Booklet My Progress

Blog Landing Page

Proof and Reasoning (Lesson 1/3)

Proof by deduction

1 / 12

Discussion

Consider the sum 1+3+5+⋯+(2n−1).

(a)

Evaluate the sum in the case n=3,4,5.

Solution:

Compute directly by adding the first few odd numbers.

For n=3:

1+3+5=9
For n=4:

1+3+5+7=16
For n=5:

1+3+5+7+9=25

So the sums are 9,16,25 respectively.

Proof and Reasoning (Lesson 1/3)

Proof by deduction

1 / 12

Discussion

Consider the sum 1+3+5+⋯+(2n−1).

(a)

Evaluate the sum in the case n=3,4,5.

Solution:

Compute directly by adding the first few odd numbers.

For n=3:

1+3+5=9
For n=4:

1+3+5+7=16
For n=5:

1+3+5+7+9=25

So the sums are 9,16,25 respectively.