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Proof of Limit Comparison Test
As 0 < c <∞ we can find out two positive and finite numbers, m and M, like m < c < M .
Now, as
we know that for large enough n the quotient an/bn should be close to c and thus there must be a positive integer N like if n > N we as well have,
m < an / bn < M
Multiplying by bn provides
Mbn < an < Mbn
provided n > N .
Here now, if ∑bn diverges then thus does ∑mbn and so as mbn < an for all adequately large n by the Comparison Test ∑an as well diverges.
Similarly, if ∑bn converges then so does ∑Mbn and as an < Mbn for all sufficiently large n by the Comparison Test ∑an as converges.
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calculate the vector LM given l(4,3),m(-1,2)
A tangent to a curve at a point is a straight line which touches but does not intersect the curve at that point. A slope of the curve at a point is defined as the
Any point on parabola, (k 2 ,k) Perpendicular distance formula: D=(k-k 2 -1)/2 1/2 Differentiating and putting =0 1-2k=0 k=1/2 Therefore the point is (1/4, 1/2) D=3/(32 1/2
At an office, the manager earns 40% more than a first year employees. The employee earns what fraction of the manager earnings?
2 times n times n divided by n
4562388/955
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Using the expample provided below, if m∠ABE = 4x + 5 and m∠CBD = 7x - 10, Determine the measure of ∠ABE. a. 155° b. 73° c. 107° d. 25° d. ∠CBD and ∠ABE are vert
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