Prove that there must be two distinct integers in A whose sum is 104.

Let A be any set of twenty integers chosen from the arithmetic progression 1, 4, 7, ...,100. Prove that there must be two distinct integers in A whose sum is 104.

Combinations Proof : The formula used to determine the number of different ways to deal n distinct playing cards to two players where each player gets at least one card.

Show that 2(2^n-1 - 1) is the formula used to determine the number of different ways to deal n distinct playing cards to two players where each player gets at least one card. I want to allow the possibility of giving a different number of cards to each player.

Fibonacci Sequence Proofs, Pascal's Triangle and Binomial Coefficients

Practice problem 1 Fn is the Fibonacci sequence (f0 = 0, f1 = 1, fn+1 = fn + fn-1). By considering examples, determine a formula for the following expressions, and then verify the formula. a. f0 + f2 + f4 + …+f2n b. f0 - f1 + f2 - f3 + …+(-1)n fn --------------------------------------------- Practice problem 3 By observation, derive a formula for (n 0) + (n 1)2 + (n 2)^2 +…+(n n)2^n = the summation n where k=0 (n k)2^k. Verify your formula. ( ) are being used to express n chose zero, n chose one … ------------------------------ Practice Problem 8 Give a formula for the Fibonacci numbers using binomial coefficients (using the identity observed in Pascal's tri... click for more

Sum of series

Determine the sum of the integers among the first 1000 positive integers which are not divisible by 4 or are not divisible by 9. (This is not an exclusive or)

Zeno's Paradox

SUPPOSE THAT A MAN WANTS TO CROSS TO THE FAR WALL OF A ROOM THAT IS 20FT ACROSS. FIRST HE CROSSES HALF OF THE DISTANCE TO REACH THE 10 FT MARK. NEXT HE CROSSES HALFWAY ACROSS THE REMAINING 10 FT TO ARRIVE AT THE 5 FT MARK. DIVIDING THE DISTANCE IN HALF AGAIN HE CROSSES TO THE 2.5 FT MARK AND CONTINUES TO CROSS THE ROOM IN THIS WAY DIVIDING EACH DISTANCE IN HALF AND CROSSING TO THAT POINT BECAUSE EACH OF THE INCREASINGLY SMALLER DISTANCES CAN BE DIVIDED IN HALF HE MUST REACH AN INFINITE NUMBER OF MIDPOINTS IN A FINITE AMOUNT OF TIME AND WILL NEVER REACH THE WALL EXPLAIN THE ERROR IN ZENO'S PARADOX.