Convert the octal expansion of (572)8 to a binary expansion.

Q: 6. The decimal expansion of 135/ 225432 will terminate after how many decimals?

A:

Q: 5. What is the decimal expansion of -? 12

A: To find the decimal expansion of 112.

Q: 7. Use Pascal's Triangle to expand the binomial (2x + 2)¹. O 16x¹64x³ +96x² - 64x + 16 - 16x4 + 64x³…

A: To expand using the Pascal triangle.

Q: 1. Use the binomial theorem to expand (m³

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Use mathematical induction to prove that 3n²+1 is divisible by 4 whenever n is an odd number.

A:

Q: Show that the sum of all  odd  integers between 1 and 1000 which are divisible by 3 is 83667

A:

Q: Convert the sum of (ABC19)16 and (19ABC)16 into its binary expansion

A: The given numbers are                                          ABC1916  and  19ABC16 Here we have to…

Q: How many bits does the binary expansion 10500 have?

A: It is known that the formula for the number of bits in a number is given by,

Q: 1- what is the binary expansion of 351? 2- what is the octal expansion of 3598? 3- what is the…

A:

Q: Show that subtraction and division are not binary operations on N.

A: Let us define subtraction operation as

Q: Use Pascal's Triangle to expand the binomial (2x - 2)*. O 16x4 16z4 64x3 96x? + 64x 16 O 16x 4 64a +…

A:

Q: Find the term with no x in the expansion of x 15

A: we have to find the term with no x in the expansion of x3+12x-215.  as we know that the (r+1)th term…

Q: Prove by mathematical induction

A: The principle of mathematical induction is a technique or method that is used to prove the statement…

Q: Prove by mathematical induction that if n is any positive odd integer, then 1 + 3n is divisible by…

A:

Q: 2k > 1+ k

A: We have to prove 2k ≥ 1 + k for every natural number k

Q: Use three terms of the expansion for √1 + x to calculate the value of √1.1018.

A:

Q: It can be shown that every integer can be uniquely represented in the form ek1341 where e=-1, 0, or…

A: We need to find balanced ternary expansion of 11 . That means , we need to find  the expansion of 11…

Q: What are the coefficients of æ5000 and æ4999 in the simplified expansion of (5æª – 2)²2021?

A:

Q: Prove that (n!)! is divisible by (n!)

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Q: Use mathematical induction to prove that any amount of postage that is an integer amount greater…

A: We have to prove that any amount of postage that is an integer amount greater than 53 cents can be…

Q: Use Pascal's Triangle to expand the binomial (2x + 2)*. O 16x4 + 64x³ + 96x2-64x – 16 O 16x + 64 +…

A:

Q: Use mathematical induction to prove that 3"7" - 2 is divisible by 8 for every non-negative integer…

A: Initial case:

Q: 10b) Determine the binary expansion of the decimal number 666. You must show your work step by step…

A: A binary number is a number expressed in the base-2 numeral system or binary numeral system, a…

Q: Find the order of [5] in Z23

A:

Q: Use Fermat's Theorem to show that n 13 - n is divisible by 2730 for all n.

A:

Q: Compute the coefficent of x8    in the expansion of (3x -2)13

A: The given expression is,

Q: Sort this permutation [5 213 4] into identity permutation [123 4 5]. Check what's the number number…

A: The permutation is nothing but the arrangement of objects in different orders. If we permute a set…

Q: Show that the weighted arithmetic mean of first 'n' natural numbers whose weight are equal to the…

A:

Q: Find the number of inversions in the permutation 436215.

A: The permutation given is 436215. To determine the number of inversion in the permutation 436215. The…

Q: 3. Convert the decimal expansion of (231)10 to a binary expansion a) (1100111), b) (1110011)2 c)…

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Q: 4. Convert the binary expansion of this integer to an octal expansion. (101101101)2

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Q: Prove that 6-1 is divisible by 5 for any n 21.

A:

Q: 5- Let consider two (02) numbers a and b with the binary expansion a=10110011 and b= 101001 what is…

A: Since you have posted multiple questions and we can answer one question. So answered first question.

Q: 1. Find the binary expansion of (233)10-

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Convert (11000 0110 0011₂ from its binary expansion to hexadecimal expansion.

A: In this question, the concept of the Number System is applied. Number System A number system is a…

Q: Find the sum of the first five natural even numbers using sigma notation.

A: We have to find sun of first 5 even natural numbers.

Q: Convert the sum of (ABC19)16 and (19ABC)16 into its binary expansion.

A:

Q: What is the coefficient of in the expansion of

A: Give the coefficient of x12x24x32x4 in the expansion of x1-x2-3x3+2x49

Q: Show that the octal expansion of a positive integer can be obtained from its binary expansion by…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Write down the first five terms of the expansion of (1 + 3x)²/½/2 for /x/ < =//=

A:

Q: Use Mathematical Induction to show that 52n -1is divisible by 8,   ∀ ∈ n N.

A: Use Mathematical Induction to show that 52n -1is divisible by 8,   ∀ ∈ n N.

Q: 1.8(a) Convert the decimal number 7510 to binary by using the sum-of-power-of-2 method. Ans:

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Q: 1. a) Convert (DEFACED),6 from hexadecimal expansion to a binary expansion. b) List all integers…

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Q: 1. Find the binary expansion of (233)10.

A:

Q: a. What is the 21st digit in the decimal expansion of b. What is the 5280th digit in the decimal…

A: Define a general formula for each digit position and use the general formula to calculate the digit…

Q: Show by induction that 21" – 8" is divisible by 13 for all n> 0

A: For the solution follow the next steps.

Q: Show by induction that 19" – 8" is divisible by 11 for all n >0

A:

Q: Find the specified nth term in the expansion of the binomial. (х — бу)5, п%3D 3

A:

Q: Prove that some multiple of 1234 has (in its base-10 expansion) at most 1234 digits, each of which…

A: Consider the numbers 0,5,55,555,.....,∑k=012335.10k . Then, by Pigeonhole principle, there are at…