Answers To The Ap Biology Lab 8

Mathematical Curiosities

2 ^ 0 +2 ^ 1 +2 ^ 2 +2 ^ 3 +2 ^ 4 +2 ^ 5 = (2 ^ 6) -1
2 ^ 0 +2 ^ 1 +...+ 2 ^ (x-1) = (2 ^ x) -1

2 • (3 ^ 0 +3 ^ 1 +3 ^ 2 +3 ^ 3 +3 ^ 4 +3 ^ 5) = (3 ^ 6) -1
2 • [3 ^ 0 +3 ^ 1 +...+ 3 ^ (x-1)] = (3 ^ x) -1

3 · (4 ^ 0 +4 ^ 1 +4 ^ 2 +4 ^ 3 +4 ^ 4 +4 ^ 5) = (4 ^ 6) -1
3 · [4 ^ 0 +4 ^ 1 +...+ 4 ^ (x-1)] = (4 ^ x) -1


[...]
11 • (12 ^ 0 +12 ^ 1 +12 ^ 2 +12 ^ 3 +12 ^ 4 +12 ^ 5) = (12 ^ 6) -1
11 • [12 ^ 0 +12 ^ 1 +. +12 .. ^ (x-1)] = (12 ^ x) -1

Conclusion
(y-1) · [y ^ y ^ 0 + 1 + y ^ 2 + .. . + and • (x-1)] = (y ^ x) -1

PS: I just discovered that this is related to the sum of geometric progressions, which I have not given yet.