21. Do the following:

(a) Find the arithmetic mean of a₁, a₂, ..., a₁₀₀, given that a₁ = 1 and
a₂ = a₃ = ... = a₁₀₀ = 100/99.

(b) Prove that 

(c) Prove that 

(d) Prove that  for all positive integers n.

22. Do the following:

(a) Find the arithmetic mean of a₀, a₁, a₂, ..., a₁₀₀, given that a₀ = 1 and
a₁ = a₂ = ... = a₁₀₀ = 99/100.

(b) Prove that 

(c) Prove that  for all positive integers n.

23. Do the following:

(a) Find the arithmetic and geometric means of the roots of x⁴ - 8x³ + 18x² - 11x + 2 = 0, given that all the roots are positive.

(b) Given that all the roots of x⁶ - 6x⁵ + ax⁴ + bx³ + cx² + dx + 1 = 0 are positive, find a, b, c, and d.

(c) Find all the roots of x¹¹ - 11x¹⁰ + ... - 1 = 0, given that each root is positive.

24. Given tht a, b, and c are the lengths of the sides of a triangle, show that

Monday, June 22, 1998