# reciprocals

1. ### Intersecting reciprocal trig functions

Hi, I hope someone can help. I'm trying to understand intuitively why y=cscx intersects y=secx at (pi/4, 1.414) and (pi/4, -1.414)? Can someone please explain why? I noticed that the parent functions of both reciprocals intersect at (pi/4, 0.707) and (pi/4, -0.707). I also noticed that 1.414...
2. ### Limit: Sum to infinity of reciprocals of factorials with alternating sign

Hello, I'm a bit stuck on this and would value your help please. I know that the sum to infinity of the reciprocals of factorials is e. But what if they have alternating sign, e.g. 1/1! - 1/2! + 1/3! + 1/4! - ... I have found the answer: identity (9) at...
3. ### weird inequalities problem with reciprocals on both sides (inequalities)

This is question number 9 of James Stewart Mathematics for Precalculus 6th Edition I already know the method where you substitute every single value from S into the equation but I was wondering if there was just a way to simplify it
4. ### help with proving trig indentity

I need to prove that cosx+cotx/secx+tanx = cosxcotx, any help would be greatly appreciated!
5. ### Why do trigonometric functions have reciprocals?

I've gotten to the point in my trigonometry studies where I am looking at Cosecant and Sine, and I see that Cosecant and Sine are reciprocals of each other. Now this means that multiplied together produce 1 (on the Unit Circle) and I'm assuming everywhere else. Now why is their relationship...
6. ### Erdos proof Sum of Reciprocals of Primes

I've been going through the Erdos proof that the sum of the reciprocals of primes is divergent. I'm having trouble understanding why there are 2^k possible ways to write the square free part.
7. ### Sum of reciprocals

Hii ! Can You help me, for this Exercice : Prove that for all integer p \geq 3 it exist p of integers natural different two to two n_1 , n_2 , ... , n_p Such as : \frac{1}{n_1}+\frac{1}{n_2}+...+\frac{1}{n_p} = 1
8. ### Sum of reciprocals of phi(p)

Write \frac{1}{1} + \frac{1}{2} + ... + \frac{1}{p-1} = \frac{a}{b}, with gcd(a,b)=1. Show that p^2 divides a if p \geq 5 I have no clue how to express it as \frac{a}{b}.
9. ### The divergence of the reciprocals of odd integers

Can anyone prove whether S = 1 + 1/3 + 1/5 + ... + 1/(2n-1) converges or diverges?
10. ### Reciprocals

When am I allowed to turn an equation or a function into it's reciprocal? Is it like multiplying by one? Can I do it any time?
11. ### Sum of reciprocals of squarefree numbers

This one is for fun. I'll give my solution later. Let S be the set of squarefree positive integers. Show, as simply as you, can that \sum_{s \in S} \frac{1}{s} = \infty. Of course an instant solution is given by the fact that the sum of the reciprocals of the primes diverges. However try using...
12. ### Sum of reciprocals of Prime Numbers

Hello, Could anyone please give me a proof using basic/elementary number theory and or calculus of the following: The sum of the reciprocals of primes is approximately equal to log(log(x)) e.g 1/2 + 1/3 + 1/5 + 1/7 + 1/11 + ... ~ log(log(x)) Thanks in advance
13. ### reciprocals

Are there 21 different positive whole numbers such that the sum of their reciprocals is 1? :) I'm not sure about this question
14. ### Variable, reciprocals, and fractions..

I came across another question which has just stumped me because I worked it over about 5 times and I couldn't figure out how the book got the answer. I've obtained messed up answers and none have them have been... Answer: 6 Problem: 2x - 3(x-2)/2 = 7 - x-3/3 The thing that probably...