Recursion – breaking a recursive relationship

I am trying to resolve the following recursive relationship
$$ K_ {2i-2} = frac {a + K_ {2i}} {1 + aK_ {2i}} quad; quad K_ {2N} = 0 $$
and $ i = 1, cdots, N $

I want to find the solution for $ K_ {2i} $.


I believe that this relationship needs to be resolved from the top down. My first attempt was to bet $ i = N $ which gives
$$ K_ {2N-2} = a $$
then $ i = N-1 $ gives
$$ K_ {2N-4} = frac {2a} {1 + a ^ 2} $$
then $ i = N-2 $ gives
$$ K_ {2N-6} = frac {a + frac {2a} {1 + a ^ 2}} {1+ frac {2a ^ 2} {1 + a ^ 2}} = frac {a ^ 3 + 3a} {1 + 3a ^ 2} $$
then $ i = N-3 $ gives
$$ K_ {2N-8} = frac {4a ^ 3 + 4a} {1 + 6a ^ 2 + a ^ 4} $$
then $ i = N-4 $ gives
$$ K_ {2N-10} = frac {a ^ 5 + 10a ^ 3 + 5a} {1 + 10a ^ 2 + 5a ^ 4} $$

I can't find a pattern in it. How can I solve this?

Python code for breaking a product from two prime numbers

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nvidia – How do I fix CUDA breaking after suspending?

As the title suggests, CUDA just doesn't work every time I wake up my laptop from an outage. I have to restart my system to get it back. To get it back after an interruption, I have to & # 39; sudo rmmod nvidia_uvm & # 39; and then & # 39; sudo modprobe nvidia_uvm & # 39; execute and of course it works, but as you can imagine, it gets old very quickly. How do I get it back permanently? If it makes a difference, I always chose a PRIME laptop with my Nvidia GPU (940MX) with the 440 drivers.

What can I do to avoid breaking the proxy rules?

My account was recently deactivated with one of the better proxy services.
This was the second time that this happened!
I have been told that my account will be blocked next time.
I don't know what I did to do this. I only scratched search engines with the rotating proxies.
I know that the catchalls I used were reported as spam 93 times and spam 78 times.
Could it be?
Should I just use a commercial catchall service (as opposed to my own) or should I drop these emails and use new ones of my own?
Maybe also, what types of platforms should I disable on SER to completely avoid this?
I really like the proxy service I use and don't want to mess it up again.
Thanks for any help.

dnd 5e – Is this homebrew metamagic feat at risk of breaking the game?

As an ex-player and GM of 3.5e, I loved the metamagic performances and I feel bad because they are not available in 5e. I want to make a self-brewed version of it, but before hollowing out my players to play with, I want them checked so that I can rebalance them if something can easily damage the game.

Here's the trick:

Metamagic magic (Requires the "Spell" ability)

Choose a metamagic option from the metamagic wizard ability and one of your known spells. You can apply this Metamagic option to the spell when you cast it, but the spell slot you have to cast to cast it corresponds to the spell level + the witchcraft cost of the Metamagic option.

You can apply this option to a Cantrip, but you must spend a magic slot equal to the cost in the witch point of the Metamagic option.

You can still benefit from "casting the spell at a higher level" for the spell, but the spending spell slot is treated as that level spell slot – the cost in the magic point of the "Metamagic" option for the spell effect.

You can do this feat multiple times, but you must choose a different metamagic option and / or a different spell

For the taste, it has the same penalties as the 3.5e metamagic exploits, and the fact that you have to spend a magic slot instead of a magic point and that you're limited to one spell per feat still makes the magician interesting. It may be a challenge, but that's why I'm here.

Related: What is the 5e wizard equivalent to the exploits "Silent Spell" and "Silent Spell" from 3.5e?

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When it is your turn, your weapon attack will break the concentration of a (hostile) slow spell.

When exactly does the magic stop influencing you?

The moment the enemy caster loses focus or the next turn? In other words, do you get your extra attacks, bonus action and the second half of your movement back immediately – in the same round?

BREAKING: Dems will receive the unedited material from The Mueller Report. When will the Americans see it?

We can only hope. For everyone else with a short attention span, some people can keep track of multiple topics related to the presidential crisis at the same time.

Just because there is a new Trump crisis does not mean that the older equally important Trump crisis news is disappearing.

Breaking down a list into several two coordinate lists

How can the following list be broken down into two separate coordinate lists?

list = {{1,{0}},{2,{0}},{3,{-2,0,2}},{4,{-2,0,2}},{5,{-2,0,2}}};

what I want to get is

list1 = {{1,0},{2,0},{3,0},{4,0},{5,0}};
list2 = {{3,-2},{4,-2},{5,-2}};
list3 = {{3,2},{4,2},{5,2}};

or

list1 = {{1,0},{2,0},{3,0},{4,0},{5,0}};
list2 = {{1,0},{2,0},{3,-2},{4,-2},{5,-2}};
list3 = {{1,0},{2,0},{3,2},{4,2},{5,2}};

or

list1 = {{1,0},{2,0},{3,-2},{4,-2},{5,-2}};
list2 = {{3,0},{4,0},{5,0}};
list3 = {{3,2},{4,2},{5,2}};

Selling Others – 6 GSA SER and 6 GSA Captcha Breaking licenses for sale

I stopped creating backlinks a few years ago and my personal licenses have disappeared. So I decided to sell it.
I offer to:
6 GSA SER licenses
6 GSA Captcha Breaker licenses
3 GSA Indexer licenses

The official price on their website is $ 99 for GSA SER, $ 147 for Captcha, and $ 20 for the indexer.
That would be an official price of $ 1,542. I'm selling mine for $ 999 (and I got permission after contacting support). So you save $ 543, or about 35%.

I am willing to sell them with a secure, trustworthy escrow account such as Safefunds. So we can both sleep well. I have 6 when I ran it on multiple machines and virtual servers.
SEMrush