From Ross: Let f0 = 0; f1 = 1,... be the Fibonacci sequence where for all n greater than or equal to 2 fn = fn-1 + fn-2. Let Q = (1+square root of 5)/2. Show that for all positive n greater than or equal to 0, fn less than or equal to Q^(n-1). Answered by Penny Nom.

My daughter had me help her with some of her college math problems that require finding the pattern. The problem was the stair problem where you can climb either 1 step or 2 steps at a time. How many combinations are there to get to the 10th step. I found the data set that solves the answer to the question, but is there an equation that expresses the answer in terms of n?

1 2 3 4 5 6 7 8 9 10 stair number
1 2 3 5 8 13 21 34 55 89 number of possible combinations

From Shameq: Hi, I've been given a problem that I'm having some trouble with. I'd really appreciate any help. Here's the question (it's called the Pay Phone Problem)

A pay phone will take only 10p, 20p, 50p, and £1 coins"(It's British).

A woman has plenty of 10p and 20p coins. She has no other coins. She can put the coins into the pay phone in any order.

INVESTIGATE the number of different ways, she could put the 10p and 20p coins into the pay phone. Answered by Penny Nom.

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