Problems on Integers: Q1-Q3 - Solutions Needed

[steve357]

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 ..

 

[HallsofIvy]

Well, what did you do? And why was this not posted under "homework help"?

 

[steve357]

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

 

[uart]

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.

 

[SammyS]

I suppose you mean k_n=[(1+(-1)ⁿ)+1]/(5n+6) .

The parentheses are important.

What you wrote literally means: k_n=\frac{(1+(-1)^n)+1}{5n}+6\,, 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.

 

[steve357]

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

 

[SammyS]

If n is odd, (-1)ⁿ = -1 .

If n is even, (-1)ⁿ = 1 .

 

[steve357]

yeah right i also got till there but what when n is in decimal??

 

[SammyS]

n is a positive integer.

It's a sequence we're talking about.