Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic
In y = ax +b when are a, -b/a, b in arithmetic progression. The
polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2
and c be in arithmetic progression?
Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1,
2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a
- b) = ab.
First prove the common difference must be even and then that it
must be divisible by 3. Think about possible remainders when the
middle number is divided by 3. Consider two cases.