Euler's number Consider, In = (1+1/n)" for all n E N. Use the binomial theorem to prove that {n} is an increas- ing sequence. Show that {n} that is bounded above and then use the Monotone Increasing Theorem to prove that it converges. We define e to be the limit of this sequence. Let x₁ = √p, where p > 0, and n+1 = √p+an, for all n € N. Show that {n} converges and find the limit. [Hint: One upper bound is 1+ 2√/p]. Let x₁ = a > 0, and n+1 = n + 1/n, for all ne N. Determine if {n} converges or diverges.
Euler's number Consider, In = (1+1/n)" for all n E N. Use the binomial theorem to prove that {n} is an increas- ing sequence. Show that {n} that is bounded above and then use the Monotone Increasing Theorem to prove that it converges. We define e to be the limit of this sequence. Let x₁ = √p, where p > 0, and n+1 = √p+an, for all n € N. Show that {n} converges and find the limit. [Hint: One upper bound is 1+ 2√/p]. Let x₁ = a > 0, and n+1 = n + 1/n, for all ne N. Determine if {n} converges or diverges.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![06:49 Mon, Apr 10 M
x
Problem 2.
MATH352HW#7Sp23.pdf
i) Euler's number Consider,
Xn = (1+1/n)n
for all n € N. Use the binomial theorem to prove that {n} is an increas-
ing sequence. Show that {n} that is bounded above and then use the
Monotone Increasing Theorem to prove that it converges. We define e to
be the limit of this sequence.
ii) Let x₁ := √√p, where p > 0, and
√p, where p > 0, and £n+1 = √p+xn, for all n E N. Show that
{n} converges and find the limit. [Hint: One upper bound is 1+2√P].
:=
iii) Let x₁ = a > 0, and n+1 = n +1/xn, for all n E N. Determine if {n}
converges or diverges.
|||
r
l 73%](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfba8c1b-379a-495a-9284-26414a9f3892%2F4d9ce9f5-de55-4318-9de6-58c2d96c49fb%2Fzsirq9d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:06:49 Mon, Apr 10 M
x
Problem 2.
MATH352HW#7Sp23.pdf
i) Euler's number Consider,
Xn = (1+1/n)n
for all n € N. Use the binomial theorem to prove that {n} is an increas-
ing sequence. Show that {n} that is bounded above and then use the
Monotone Increasing Theorem to prove that it converges. We define e to
be the limit of this sequence.
ii) Let x₁ := √√p, where p > 0, and
√p, where p > 0, and £n+1 = √p+xn, for all n E N. Show that
{n} converges and find the limit. [Hint: One upper bound is 1+2√P].
:=
iii) Let x₁ = a > 0, and n+1 = n +1/xn, for all n E N. Determine if {n}
converges or diverges.
|||
r
l 73%
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