Prove or Disprove that: If a > 0 and b are two rational numbers, then a'...
Prove that is an integer for all n > 0.
Use induction to prove that 0–0 4j3 = n4 + 2n3 + n2 where n > 0.
{x_n} and {y_n} are sequences of positive real numbers AC fn→oo > O, prove tha m in yn lim xn 0 implies lim yn_0
| Prove that for n e N, n > 0, we have 1 x 1!+ 2 x 2!+... tnx n! = (n + 1)! - 1.
Exercise 6. Show that if f(x) > 0 for all x e [a, b] and f is integrable, then Sfdx > 0.
Prove or Disprove: Let p E P(F) and suppose that deg p > 1 and p is irreducible. Then p(a)メ0 for all a E F.
Problem (2), 10 points Disprove the following statement: If m > 2 is an integer, then (a + b) (mod m) = a (mod m) +b (mod m) for all integers a and b.
Use induction and Pascal's identity to prove that (7) = 2" where n > 0.
A= 10 5 5 2 B= 4. 1 > ,A+B= . ] 0
Show the resistance looking into the base ro= 0 PA + B + 1)RE >RE (b)