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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.
Retail price index This is weighted average of price relatives based on an average household in the base year. The items consumed are divided into groups as liker food, transp
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Let Xn be a sequence of distinct real numbers. Define E = {L : L is a subsequential limit of Xn}. Prove E is closed.
real numbers?
If secA= x+1/4x, prove that secA+tanA=2x or 1/2x. Ans: Sec? = x + 1/4x ⇒ Sec 2 ? =( x + 1/4x) 2 (Sec 2 ?= 1 + Tan 2 ?) Tan 2 ? = ( x +
creative assignment about sets
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fig angles of a irregular polygons exterior and interior .
importance of lp
even numbers
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