Question 2: Which of the following sequences are increasing, decreasing, or bounded? (-1)" Gn = 5 - - H, = , In = n* n2 Jn = sin (), K„ =(-5)", Ln = 3-" %3D

Q: What is the probability that given a block n of 30 bits, that you have an error sequence E(X)=P(X)…

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Q: Homework: Find the following 1. L1 (s+ a)2)

A: As per our guidelines we are supposed to answer only one question

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A: Dear student. You have posted many questions. In our policy, i have answering the first question. If…

Q: (3) Find 125 * dx I- e

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Q: ^n for all n>=6

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Q: +00 For what values of x do the power series (-1)"-1^_ converges. n=1

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A: We have to find whether the given series converges or diverges?

Q: M 1 {[1 '* . _ (w/wn)²]² + [2¢w/wn] 1/2 2 1²}' ||

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Q: Use this function to show that 1+(1/3^2)+(1/5^2)+...=pi^2/8   f(x)=.5-(Summation from

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Q: What does the nth term test determine for the summation of (e^n)/(e^n+n) from 0 to infinity?

A: We are given the expression,

Q: Let U1, U2, ... be i.i.d. Uni(0, 1) random variables. - log U; is distributed as exp(1). (2) Find…

A: 1) From the given information,  U1, U2, ....... be i.i.d Uni(0,1) random variables. Given that…

Q: 1. Test each of the following series by the ratio test. 1/2 + 2(2^2) + 3/(2^3) + 4/ (2^4)... 2.…

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Q: Series n=1 100 on top 1/n^2+n

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Q: {b_n}={3^n/n!}

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Q: 1. Consider the matrices A₁ 4 = ( 1 ) - 1 3 0 A₂ 42 = (3-2) ₁ 4₁ = ( 2² -2²), , A3 0 -2 These…

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Q: 2) is E=1 2n convergent?

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Q: Given α=0.06α=0.06, zα/2=z0.03=1.88zα/2=z0.03=1.88, ˆpi=0.77p^i=0.77, and n=150n=150 compute the…

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Q: (-5) 1 Find the sum of the series 6T

A: The given series is an infinite geometric series and its sum is S=a/1-r,r<1.  See 2nd step.

Q: o find the unique solution p^∗ ∈ [0, 1] of the equation x^3 + 6x^2 − 4 = 0, rewrite the equation in…

A: To find the unique solution p*∈[0,1]  of the equation  x3+6x2-4=0 Here we need to rewrite the…

Q: infinity Σ(cos^-1 (3/n+5) - cos^-1 (3/n+6)) n=1 Sn = ?

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Q: Show that if a and b are constants, then E[aX+ b] = aE[X] + b.

A: We have to show that ,We know that for a discrete variable following properties will hold :

Q: If the ratio of boys to girls in tennis camp is 3:5 if there are 64 campers, how many are girls 

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Q: Use limit comparison test for sum of n=1 to ♾ of (3n^3+2)^(1/2)/(8n^2+9n+1)

A: take bn = 1/n  we know that if limn→∞anbn= finite  then by limit comparison test both series behave…

Q: (1) List the first 5 terms of oach of the soquence (a,). n+1 (d) an = sin An = 3n- - 1 3(-1)" (e) a…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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Q: What is the second derivative of the power series y = En-o Cnx"? 00 O y" = E Cnnx"-1 n=D1 O y" = E2…

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Q: Series n=0 5 on top.  n!x^n.   0!=1

A: Solution is given below:

Q: Define Power Series e^x?

A: we know that ex=1+x+x22!+x33!+............=∑n=0∞xnn!                                      ..1

Q: what is the summation where k = 1 of e^-2k

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Q: 27 Find (all) the value(s) of c such that 3c2n 8. %3D n=0 (A) c=3 (B) с 3 4 (C) c=-33 (D) c = } (E)…

A: Substitute the value of c as 0, 1 and 2 in the nth term to find the generated series.

Q: Maclaurine’s series of ∫((cos^2(x) dx)

A: To find → Maclaurine's series of ∫ cos2 x dxSolution →                       ∫ cos2x dx = ∫ 1+cos…

Q: Which one of the following .10 sequences converges to_0 An = tan'(n) An = 2 %3D An = 2 (In n)² V An…

A: Given: We have to check which one of the sequences converges to 0

Q: Consider the following six sequences: Cn = n², dn 6n + 4 7n 3' Wn = n Un - = (-²) * · (27). —2)", Zn…

A: The objective of the question is to analyze the given sequences in terms of monotonicity,…