= a O a = a for all positive integers a. = a O b = b O a for all positive integers a and b. = If a > b> 1, then a b = (a - b) O b. Compute the value of 16 O 2018.

Q: 13. If a is an algebraic integer satisfying a + a + 1 = 0 and ß is an algebraic integer satisfying…

A: Given: α is an algebraic integer satisfying α3+α+1=0 and ß is an algebraic integer satisfying…

Q: Evaluate if x=4,8,3,-2 ∑x ∑x+1 ∑(x+1) 3∑x - 4

A: Given that  if x=4,8,3,-2

Q: An operation * is defined on the set of real numbers by a * b = a + b – ½ ab. What is (3 * 2) * 2? *

A: The rational number and irrational number are together called real numbers. An operation is a rule…

Q: Fill in each blank so that the resulting statement is true.

A: We have, 3x=π4+nπ  for any integer n.

Q: З and an - - 3ап-1 + an-2 for integers n>2. Evaluate and d4: Let a, = 2, a2

A:

Q: Evaluate the combination. C(44,22)

A:

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

A:

Q: Determine whether the statement is true or false. Justify your answer with a proof or…

A: Yes, the product of  even integer and any integer equal to even

Q: Evaluate -2セ 34 L{+(e 2te

A:

Q: Provide an estimate for each very large or very small quantity.  Express your estimate as a single…

A:

Q: Find the product of all positive integers from n down through 1 for n = 5.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Remainder must always be either less than or equal to the divisor. true or false

A: Remainder must be either less than or equal to the divisor . The above statement is true .

Q: Find x if x is not -6, and 9/12 = 5/(6+x). ______________

A: The equation 912=56+x

Q: Find (2+j5) O 0.00934 - j0.265 O 0.0265 - j0.00934 O 0.00934 -j0.0265 0.265-j0.00934

A: Solution:-

Q: IV. Find the sum of the squares of the 1st In consecutive positive integers. A. Sum of the lat 12 B.…

A:

Q: Simplity. Assume all exponents are positive integers. 35n 45x² 2. 35n² 25x 1. 4. p²-3p-54 p-9 5.…

A:

Q: Expand and simplify the expression: (x² + e-2x In (e*+1) ex

A:

Q: For any integer a, show that a²-a+7 ends in one of the digits 3, 7, or 9.

A: For any integer a , we have to show that a2 - a + 7 ends in one of the digits 3 , 7 , or 9 . Note…

Q: Vx x² >0

A: Integer, whole-valued positive or negative number or 0. The integers are generated from the set of…

Q: 16 (; + ; ++) for every positive integers a, b,c,d. O True

A: Given that: a, b, c, d are positive integers.

Q: using the digits 2 through 9, find the number of different 5 - digits numbers such that  a. digits…

A:

Q: = 55. Determine the value of n if (5)

A:

Q: . n > 5 only if n > 7.

A: Given that n>5 only if n>7

Q: Express each terminating decimal as a quotient of integers, reduced to lowest terms. 0.45

A: Given Decimal  = 0.45

Q: Identify the expression of a for which the following equation holds for every positive integers n…

A:

Q: #5 Find An if n is a positive integer and A = 4 -3 - 2

A:

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.