Problems on Integers: Q1-Q3 - Solutions Needed

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The possible values of n are 1, 2, 3, 4, ... .So, the question is: "What is the smallest value of n for which 1/(5n+6)>1/100 ?", which you can solve on your own. In summary, the conversation discusses finding the number of terms in a sequence that satisfy certain conditions and also finding the sum of fractions within a specific range. The conversation also touches upon finding the greatest common divisor and least common multiple of a pair of natural numbers. The individual seeking help had difficulty with the questions and sought assistance.
  • #1
steve357
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Q 1:-
Given a sequence kn=[(1+(-1)^n)+1]/5n+6..
find the no of terms of the sequence kn which will satisfy the condition kn lies between 1/100 and 39/100.

Q 2:-
Find the sum of all the irreducable fractions between 10 and 20 with a denominator of 3

Q 3:-
Find all pairs of natural no s whose greatest common divisor is 5 and L.C.M is 105

i could really not do much about these so please help! Any assistance appreciated ..
 
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  • #2
Well, what did you do? And why was this not posted under "homework help"?
 
  • #3
See i don't know anything about forums..like where do we even get the section "homework help"..! anyways that's not the issue here.
For the first question i tried to make the denominator 100 for which i got n in fraction now that if i put in numerator then in all probability it becomes a question of complex numbers which i don't know.For the second i am getting the answer uncountable or infinity and i don't know third
 
  • #4
kn=[(1+(-1)^n)+1]/5n+6
Find the no of terms of the sequence kn which will satisfy the condition kn lies between 1/100 and 39/100.

There are none, as all the terms in the sequence are greater than 6.
 
  • #5
I suppose you mean kn=[(1+(-1)n)+1]/(5n+6) .

The parentheses are important.

What you wrote literally means: [itex]k_n=\frac{(1+(-1)^n)+1}{5n}+6\,,[/itex] which is how uart likely interpreted it.

There are many numbers between 1/100 and 39/100 which don't have a denominator of 100.

How many terms of the sequence are between 0.01 and 0.39 ?

The terms of the sequence with n odd look much different from the terms with n even.
 
  • #6
There are many numbers between 1/100 and 39/100 which don't have a denominator of 100.

[/QUOTE]
yeah but i was trying to first find that n for which i shall get the limiting values;i mean 0.01 and 0.39. And i did not understand what you said in the second part
 
  • #7
If n is odd, (-1)n = -1 .

If n is even, (-1)n = 1 .
 
  • #8
yeah right i also got till there but what when n is in decimal??
 
  • #9
n is a positive integer.

It's a sequence we're talking about.
 

Related to Problems on Integers: Q1-Q3 - Solutions Needed

1. What are integers?

Integers are whole numbers that do not have any fractional or decimal component. They can be positive, negative, or zero.

2. What is the difference between positive and negative integers?

Positive integers are numbers greater than zero, while negative integers are numbers less than zero. The sign (+ or -) indicates whether the integer is positive or negative.

3. How do you add and subtract integers?

To add integers, you can use the number line to visualize the addition. If the integers have the same sign, add their absolute values and keep the sign. If they have different signs, subtract the smaller absolute value from the larger one and keep the sign of the integer with the larger absolute value. To subtract integers, you can add the opposite of the second integer to the first integer.

4. What are some real-life applications of integers?

Integers are used in many real-life situations, such as counting money (positive integers for income and negative integers for expenses), measuring temperature (positive integers for hot temperatures and negative integers for cold temperatures), and keeping track of points in a game (positive integers for points earned and negative integers for points lost).

5. How do you solve word problems involving integers?

To solve word problems involving integers, you can follow these steps: 1) Identify the unknown quantities and assign variables to them. 2) Read the problem carefully and determine the operations needed to solve it. 3) Write an equation or inequality using the variables and solve for the unknown quantity. 4) Check your solution to make sure it makes sense in the context of the problem.

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