If x1, y1, are two positive unequal numbers and xn = (xn-1+ yn-1)/2 and yn= sqrt(xn-1yn-1)  for all n>=2, Prove that the sequences and  are monotonic and they converge to the same limit. *Prove each step

Q: For each sequence {an}1, prove it converges by showing that it is bounded and mono- tone, and find…

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Q: ter n minutes, the temperature of a cup of coffee, in degrees Celsius, is T 55 + 25e0.1n %3D e0.1n

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Q: Prove that the sequence ((-1)")=1 does not converge to any number.

A: Solution :- The given sequence is                          {  an }   =   { (-1)n}  then , we have to…

Q: Find the limit of the sequence {an} = {-Yón}. Enter as an exact value. V 4n+1 limn→o An help…

A: To find the limit of a given sequence.  {an}.

Q: h(x)= 4/5 x5 +3x4 -7x3 -15/2 x2 +20x+1 local max & local min?

A: Given that To find local max and local min

Q: Prove that sequence {an}= {(-1)n} does not have a limit.

A: According to the given information it is required to show that {an}= {(-1)n} has no limit.

Q: If xi > 0 and xn+1 := (2+ xn)¯' for n> 1, show that (x,„) is a contractive sequence. Find the limit.

A: We only solve one problem at a time so please submit the next question separately which you want to…

Q: what is the absolute min and max for the following; f(x)=x^2-4x+6 with [1,4)

A: To find the absolute minimum and maximum of the function f(x) = x^2 - 4x + 6 on the interval [1, 4),…

Q: Find the third term of the sequence  {2n^2/3^n-1}from n=1 to ∞

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Q: Find a sequence of real numbers {a;} such that lim a, does not n-00 xist, but it has 3 subsequential…

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Q: Let (an) be an increasing sequence of real numbers bounded from above and (bn) be a decreasing…

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Q: Find the Limit of seqvence d Sz, Sz5z, J2552 ---

A: The sequence is 2, 22,222,…. That is, the terms of the sequence can be written as,…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.