(b) If m < a1 + ... + an < M n, and v, is positive and + anVn < Mv1. + anUn| < Mvi Vn. decreasing, then mvị < ajvi + ... (c) If in (b) |Sn| < M Vn, then |a1v1 + ... + anVn| < Mv1 Vn.

Q: Find all values of z for which z* + 2 – i2v3 = 0 and represent them geometrically.

A:

Q: Prove that (1, 2) (1,(1), 2, 3).

A: We know, if A and B are two sets then, A is subset of B  if every element in A is also in B.

Q: Find all numbers z such that Az3 + Bz² + Cz = D %3D B = [2 4 21 1 1 1. A = 1 3 1. 1 -2 2 4 21 C li 3…

A:

Q: . Prove that an→L = Jan] → |L]. (Make cas

A: Given that an is a sequence which converges to L that is, an→L. Then we have to prove that |an|…

Q: don't understand how the equation turned into 5x+x+6/x(x+6), could you go through the equation again…

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Q: The Fibonacci numbers 1, 1, 2, 3, 5, 8, 13.. are defined by the recursion formula xn+1 = Xn + xn-1,…

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Q: Show that if a and b are real numbers and a!=0 then there is unique number r such that ar+b=0

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Q: Determine all the roots of z +1 = 0

A: The given question is related with complex analysis. We have to determine all the roots of z4 + 1 =…

Q: From Leibnitz theorem °C=

A:

Q: 5 Find

A: To find the integral, first use the sum and difference rule and separate the integral.…

Q: verify that (A + B)T = AT + BT

A:

Q: Show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

A: To show that the group &lt;a, b | a^5 = b^2 = e, ba = a^2b&gt; is isomorphic to Z2, we need to…

Q: 5x+h over 5x+h+3 minus 5x over 5x+3, all over h. This is a difference quotient problem in…

A: LCD of the numerator is (5x+5h+3)(5x+3).We make both denominators same then subtract the rational…

Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

Q: Show that is isomorphic to Z2.

A:

Q: Prove that product notation d/n = nτ(n)/2.

A:

Q: Let H = {(1), (12)(34), (13)(24), (14)(23)}. Find the left cosets of H in A4 (see Table 5.1 on page…

A: Given H = (1), (12)(34), (13)(24), (14)(23) in A4 H =4and A4 =4!2 =12 So , Number of distinct left…

Q: Solve the initial value problem below using the method of Laplace transforms. y" - 4y' - 12y = 0,…

A: Given equation is: y"-4y'-12y=0 ,y(0)=1,y'(0)=38 We have to find the value of y(x)

Q: b22 Such that/2/-1E andArg 4.

A: We find complex number

Q: verify that (AT )T = A

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Q: xʻy Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (x4+6y8) r4.

A:

Q: Compute the following values, showing your work: φ(20), φ(25), φ(54) and φ(8!)

A:

Q: beta

A: According to the question,        First,  define some of the terms for…

Q: Section I.. -x+3 if x>! Let f(x)= 2. if Osx<l ,state the domain. x2 if x<0

A: Here the piecewise function is given that  F(x) =.  3 - x.       If x&gt; 0               2.…

Q: Find the Polah farm of Z=(-1+)

A:

Q: -1 Let A = 01. Compute A100 -2 1 1 3.

A: To compute the A100 first we need to diagonalize it to make the computation very easy.

Q: Show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

A: We have to show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

Q: nd y axsis labelled ?

A: Morphospecies on A Morphospecies on B Morphospecies on C 7 13 3 7 9 4 2 4 4 4 4 2 11 14 10…

Q: 1. Prove that fraction where m is z-4

A: Given: zn-1z-1 ⇒zn-1nz-1 ----(1) Let apply the limit in equation (1) limz→1zn-1nz-1 ----(2) Let n=pq…

Q: 1) D Prove that 224 O 210

A:

Q: Prove that Z(D,) # {1} if and only if 2|n (hint: if 2|n look at ri).

A: Let us suppose, Dn=e,r,r2,..,n-1,f,rf,..,rn-1f and nis divided  by 2. Then, n2 is a integer. We see…