Use the Geometric Sum identity to prove that, if r 70, then (1 – x)3 1 =1+ (1 - x) + (1 – x)² + |

Q: (a) For every integer n, the number n² — n must be even. (b) For all real numbers a, a² < a¹. (c)…

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Q: The sum + is between 8 (A) and 3 (B) and 1 (C) 1 and 1 14/ D) 1 and 1/2 E) 1 and 2

A: The given is  Sum of this can be calculated  as           =                         =…

Q: Show that if x > 0 and |x² – 9| < 2, then |x - 3| < 1.

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Q: 10 a.) Completely simplify E ()2* i=0 b.) Expand (1 – r)® and simplify. c.) Expand (r +r-1)5 and…

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Q: Find the adjoint of the operation B = 2|0 × 1|- ; | 1 ×o |

A: This question asks to find the adjoint of the operation B^=2|0×1|-i|1×0|.

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: given 7(x-1)=2(3x+2) prove x=11

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Q: Find the Domain of 1, if f(=) 0(s-6) %3D O Domain: y is all real numbers O Domain: y N0 O Domain: NO…

A: Given f(x)=6(x-6)2 To find f-1, assume y=f(x) then swap variables to find f-1

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

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Q: (b) Given integers a, b and c such that cla and cb then c|(ar + bs) for all r, s E Z. True False &…

A: Given that c|a and c|b for some given integers a,b and c The statement is c|ar+bs for all r,s∈ℤ…

Q: Prove that if |x-1| < 1, then x² - 2x + 5| < 8.

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Q: Show that * y = (y² – r*)(2² – x*)(2² – y³)

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Q: Suppose SCR is a set of numbers. (a) Define inf(S) and sup(S). (b) Show that inf(S) = - sup(-S). (c)…

A: Set: A well-defined collection of objects or numbers is called a set. We can write a set in two…

Q: Let x = 2 and y=3. Compute 7 ||x - y||₁ = ||x - y||∞o = ||x - y||₂=

A: Given :- x=-527,y=231

Q: Find the term of (a – 2b)3 that has b in it. |

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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.