I like the pigeonhole principle too its pretty easy to comprehend
It can be used in very complicated situations. Consider the following problem:
Let A = (a1, a2,..., a2000) be a sequence of integers each lying in the interval [−1000,1000].
Suppose that the entries in A sum to 1. Show that some nonempty subsequence of A sums to zero.
2=3
0.99999 etc. =1
Both of these can be proven true believe it or not
BOTH OF THESE CAN BR PROVEN TRUE ?!
THE SECOND ONE
0.9999999999...... =1
IS TRUE !
1+1=3!!!
(NOT!!! I am being a DUMMY!!!)
just use AM>= GM.
What's the sum of all natural numbers?
Spoiler: the answer is crazier than the question
Old post, but it's -1/12. The proof is based on Zeta Function Regularization, I think Euler did it.
Here's a proof that 0.99999... = 1
0.999999... = 0.9+0.09+0.009...
a1=0.9, r=1/10
Based on the Infinite Geometric Sum formula S = (a1/1-r):
0.9/(1-1/10) = 0.9/(9/10) = 9/9 = 1
Ummmmmmmmmmmmmmmmmmmmmmmmm.........okay.
Let me calculate.
.......
(24 hours later)
Correct! I THINK...
2 1
x 2 9
_______
1 8 9
4 2
_______
6 0 9
Solve for X
@TylerMTL: 2 * 29, add a zero to the outcome and add 29 to the result.
@LongIslandMark: that seems to imply that the method for calculating the surface area is incorrect. When the volume clearly has a limit, so must the surface area have one.
21!
1800-666=1134
What?