Answer Happy

1. Write the sum in sigma notation and use the appropriate formula to evaluate it. (The final answer is large and may be left with exponents.) 3+3.5+3.5² +3.5³ + +3.523 2. Prove that for all integers n ≥ 0, ... 20+2¹+22+ +22+1 1. 3. Prove or give a counterexample: if a (b + c), then a | b and a | c. 4. How many solutions are there to the equation x₁ + x₂ + x3 + x4 + 5 = 79 where the x, are nonnegative integers with ₁ ≥ 2, 3 ≥ 4, and 4 ≤ 7? 5. Using the fact that 8-7 = 56: (a) Find the inverse of 8 modulo 55. (b) Use (a) to solve the congruence 8x = 4 (mod 55).