Question

please can someone help me with solution to measure theory and integration question???

Answer 1

find the length of the set \[\cup_{k=1}^{\infty} \left\{ x:\frac{ 1 }{ k + 1 } \le x \le \frac{ 1 }{ k } \right\}\]

Answer 2

please help

Answer 3

What is the first step do you think you should do?

Answer 4

i don"t know

Answer 5

Have you done questions like this before?

Answer 6

@GIL.ojei

Answer 7

no

Answer 8

@tboi

Answer 9

So, what I would is look on the internet like google for examples to questions like that, ok?

Answer 10

@GIL.ojei

Answer 11

please solve this first, that will also give me a clue

Answer 12

Sorry it is against the code of conduct to give out direct answers.

Answer 13

you are not giving out answers, you are giving a prove . which includes statements and directions too

Answer 14

I know but I cant do that I have to let you do it and find the answer your self, I am so sorry but all i can do is guide you toward the answer.

Answer 15

ok. please guide me . what should i do?

Answer 16

Ok first what I would do is simplify the equation to make it easier to solve. Tell me when you are done doing that.

Answer 17

simplifing, i got k
≤
-1 and k
≤
1/x

a few moments ago

Answer 18

@mathmale here he can help ok I have to go I hope you get what you need.

Answer 19

@GIL.ojei: My first suggestion would be that y ou let k=1 and write the resulting inequality, then k=2, do the same, for k=1 to 5 or 6. These concrete examples should give you an idea of what the set in question looks like. Please share any work you do.

Answer 20

ok. i will post my result soon. thank you very much

Answer 21

For k=1 in the function I have , 1/2 <=x<=1 and for k=2, I have 1/3<=x<=1/2 and it continues that manner. So what will be my conclusion sir?

Answer 22

What next should I do or how should I conclude the the length?

Answer 23

@mathmale

Answer 24

@mathmale

Answer 25

@mathmale

Answer 26

@jabez177

Answer 27

@ganeshie8