Calculus II
Contents
Series
Integrals
Definite integrals
Some primitives
Numerical methods
Exercices
© The scientific sentence. 2010
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Calculus II: Sequences
Exercises
A sequence is a list of numbers written in a specific order.
The infinite sequence has an infinite number of terms.
The general term of a sequence is denoted as an
and the serie as {an}
1.
Write the three first terms and the 10th term
of the following two infinite sequences:
a) {(n + 1)/n2}
b) {(-1)n+1. 2n+1}
2.
Write the sequence {1/√n}
as a function and graph this function.
What i sthe limit of this function when n tends to ∞ ?.
3.
The Squeeze Theorem for Sequences tells us:
For three sequences {an}, {bn}, and {cn}
with an ≤ bn ≤ cn for all sufficiently large n
If
| lim an = | lim cn = L |
| n → ∞ | n → ∞ |
Then
lim bn = L
n → ∞
an = {(n + 1)2/n2}
bn = {(n + 2)/n}
cn = {((n + 1)/n}
Apply this theorem to show that
lim bn = 1
n → ∞
Solutions
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