A hypothetical example: You have a 1/1000 chance of being hit by a bus when crossing the street. However, if you perform the action of crossing the street 1000 times, then your chance of being ...

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 …

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 …

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 …

For the congruence modulo $4$ you don't even need to invoke Euler's Theorem; you can just note that since $2^2\equiv 0\pmod {4}$, then $2^ {1000}\equiv 0 \pmod {4}$.

What do you call numbers such as $100, 200, 500, 1000, 10000, 50000$ as opposed to $370, 14, 4500, 59000$ Ask Question Asked 13 years, 11 months ago Modified 9 years, 6 months ago

well, do you know how to compare $n^ {-10}$ and $ (n+1)^ {-10}$? can you see how small $2^ {-10}$ is compared to $10^ {-3}$?

$3^ {10}+3^ {100}+3^ {1000}+\dots \equiv 3\cdot 3^ {9}+3\cdot 3^ {99}+3\cdot 3^ {999}+\dots$ $\equiv 3\cdot (-1)+3\cdot (-1)+3\cdot (-1)+\dots\pmod {7}$ Again using the fact that we can replace …

May 13, 2014 · 1 the number of factor 2's between 1-1000 is more than 5's.so u must count the number of 5's that exist between 1-1000.can u continue?

Determine precisely how this pattern proceeds, and you'll be able to say what each of $3^ {1000},3^ {10000},3^ {100000}$ are (modulo $7$), which will tell you what their sum is (modulo $7$).