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I have seen a proof before. It goes like this...
Grandi's series:
S1:
2S1 (shift the second series one column):
180,081
Hello,
Hello;
When sin(x) = y, one solution is x = sin^(-1)(y), also written asin(y)
You should be getting 3/4 when you have done it right
Yes, that is implied in the last sentence. Also, the very first jump must be forwards
Reminds me of the story of how Newton read Descartes' Geometry. He read a little bit, went back to the beginning, read a bit further, and continued until he had memorised the whole thing. Clearly he thought it was important.
Euclid's Elements is something that until contemporary times every educated person was expected to have read, though it's not exactly comprehensive.
If you want a comprehensive self-taught resource for mathematics, I suggest you look to the Internet (and do problems!) There will be instructive videos on the vast majority of topics you encounter if you search YouTube for them. Khan Academy is an example of what I'm thinking of; there are hundreds of videos covering mathematics from 0, and practice modules.
Hello;
Hello again!
For 2. Bobbym is correct. The mistake you made was to keep track of every single letter when in fact there are a lot of duplicates. In fact, there are four pairs of matching letters, and 2^4 = 16, so you counted each arrangement 16 times. This is why, when you divide your answer by bobbym's, you get 16.
Your method would work if every letter is different, but when there are identical letters you have to divide by the number of identical arrangements..
Aren't there several ways to solve it? I think the question might be why does it need to be solved. I would say it is just a formality to clarify what the function is getting closer to in that direction. Also, I have heard infinite limits and sums show up all the time in quantum physics.
Hello!
3. The probability is:
You get 7/40 from multiplying the chance of each step in any sequence that leads to one bad chip (e.g. 7/10*6/9*3/8 for the third chip being bad or 3/10*7/9*6/8 for the first). Then multiply 7/40 by three since there are three ways to do this (first chip, second chip, or third chip is bad).
4. You need to multiply the conditional probabilities together. When she buys an ice cream 80% of 70% of the time, you multiply those two together. So we get:
Hello
123 * 95! = 1270587354053404289299763358225551432733922799834436862913106820261818160474148484359227141172407209633283715134299872704101089280000000000000000000000
About 1.27 * 10^150
I have noticed that every 5 posts, at least one trailing zero is added (but it is too trivial to pursue further right now)
And just so we're getting our post number:
Hello!
1. E is the difference between the values and the mean, or in other words it is the half the difference between the two. P is just the mean.
I get 0.109-0.023 < p < 0.109+0.023
So can anyone give a reasonable explanation of why this game is worth four dollars, an infinite amount, minus 50 cents, minus 8.3 recurring cents, or something else? Lol