Chapter 6 Sequences And Series Flashcards
What is the goal of mathematical induction?
To prove that a statement involving an integer n is true for all n > 0.
What is the first step in a proof by induction?
Prove that the result is true for an initial value n = 1.
What do you assume in the induction step?
Assume that the result is true for some general value n = k.
What must you prove in the induction step?
Prove that if the result is true for n = k, then it is true for n = k + 1.
What is a series?
A series is the sum of the terms of a sequence.
How can the general term of a sequence be represented?
The general term of a sequence may be written as a_n or u_n.
What notation is often used for the terms of a sequence?
The terms of a sequence are often written as d_1, d_2, d_3, … or W_1, W_2, W_3, …
How can some series be expressed?
Some series can be expressed as combinations of standard results.
