Find the least positive integer n for which 2n + 5n - n is a multiple of 1000.

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A: NOTE: Refresh your page if you can't see any equations. .

Q: (f) The sum of the squares of the odd integers between 0 and 100.

A: Explained below

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A: Given,           fx=13x4+x2

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Q: *-

A: Given: 3x=π4+nπ

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A: The objective is to prove the given statement using induction

Q: 2"-1 for positive integers n. 2n

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Q: Find the sum of all four-digit numbers that can be formed by the digits 1, 3, 5, 7, 9 without…

A: Answer: Option b)  666600

Q: The product of any integer and 2 is greater than 2.

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A: We prove this by induction.

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A: We will find out the required solution.

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A: In this question, tne concept of sum of first positive even integers is applied.

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A: Given sum is  a+2a+3a+4a+5a+6a+7a+8a+9a

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A: Let us  solve the question in the next step.

Q: How many positive integer solutions are there to x1 + x2 + x3 =15 ?

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Q: (c) Show that for 2" > 4n for n ≥ 5.

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Q: The sum of the digits in the number 56 is 11. (5+6=11) a) Show that the sum of the digits of the…

A: a) Sum of the digits from 15 to 18 1+5=6 1+6=7 1+7=8 1+8=9 Now 6+7+8+9=30

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Q: How many zeros are there at the end of 1001?

A: This question is related to Number Theory

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.