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algebra precalculus - Which is greater: $1000^ {1000}$ or $1001^ {999 . . . The way you're getting your bounds isn't a useful way to do things You've picked the two very smallest terms of the expression to add together; on the other end of the binomial expansion, you have terms like $999^ {1000}$, which swamp your bound by about 3000 orders of magnitude
If you toss $1000$ fair coins $10$ times each, what is the probability . . . Essentially, $1000 1024$ is the average number (or "expected" number) of coins that will have come up all heads, but that includes the cases where more than one coin comes up heads all the time, so it doesn't work as a probability Consider the case where you flip two coins once each What is the odds that one coin ended up heads?
What does X% faster mean? - Mathematics Stack Exchange 29 I was reading something today that was talking in terms of 10%, 100% and 1000% faster I assumed that 10% faster means it takes 10% less time (60 seconds down to 54 seconds) If that is correct wouldn't 100% faster mean 0 time and 1000% mean traveling back in time?
Finding the remainder of $N= 10^ {10}+10^ {100}+10^ {1000}+\cdots+10 . . . $3^ {10}+3^ {100}+3^ {1000}+\dots \equiv 3\cdot 3^ {9}+3\cdot 3^ {99}+3\cdot 3^ {999}+\dots$ $\equiv 3\cdot (-1)+3\cdot (-1)+3\cdot (-1)+\dots\pmod {7}$ Again using the fact that we can replace multiplicands with something they are equivalent to Now, we make normal arithmetic simplifications:
What is mathematical basis for the percent symbol (%)? Percent means 1 part of 100 or 1 100 and is indicated with % Per mille means 1 part of 1000 or 1 1000 and is indicated with ‰, so it seems that these symbols indicate the mathematical operations