2/2 00 (-1)" (2n + 1)³' COs nx 1°) Show that dr = Justify your reasoning. n=1
Percentage
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Algebraic Expressions
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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.
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Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
P14 Calc II
![Definition. Let f1, f2, f3, ... be a sequence of functions defined on an interval I. The
series > fn(x) is said to have property C on I if there exists a convergent series of
n=1
positive constants, Mn, satisfying |fn(x)| < Mn for all values of n and for every x
n=1
in the interval I.
Theorem. If the series > fn(x) has property C on the interval [a, b], and if the terms
n=1
fn(x) are continuous functions on [a, b], then
cb 0o
Σ) r =Σ r) dr.
D.
n=1
n=1
(-1)"
(2n + 1)3 '
=/2 00
COs nx
dx =
n2
1°) Show that
Justify your reasoning.
n=1
2°) Suppose that fi, f2, f3, . .. are continuous functions on the interval [0, 1] such that, for
each r € [0, 1] and for all natural numbers n,
E fa(x) = nxe-n=².
k=1
Prove that the series fn(x) does not have property C on [0, 1].
n=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f17e2b2-af53-4156-a6eb-e12aa0abf439%2Fd36ed391-5963-4355-ac71-35072f3bccb5%2F9rsv26_processed.png&w=3840&q=75)
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