Math Is Fun Forum

1) Let S be the sum of a finite geometric series with negative common ratio whose first and last terms are 1 and 4, respectively. (For example, one such series is 1-2+4, whose sum is 3.)

There is a real number L such that S must be greater than L, but we can make S as close as we wish to L by choosing the number of terms in the series appropriately. Determine L.

2)If  a/b rounded to the nearest trillionth is 0.008012018027, where a and b are positive integers, what is the smallest possible value of a+b?/

For math class homework, I have several problems like this and I don't really know how to do these:

Let g(x) = x^4-5x^3+2x^2+7x-11, and let the roots of g(x) be p, q, r, and s.

(a) Compute pqr + pqs + prs + qrs.
(b) Compute

(c) Compute p^2 + q^2 + r^2 + s^2.
(d) Compute p^2qrs + pq^2rs + pqr^2s + pqrs^2.

Can you help me understand the method, not just do them for me?

Thanks!

(a) Give an example of two irrational numbers which, when added, produce a rational number. (sqrt(2) and -sqrt(2) )

Now let's consider just the addition of radicals.

(b) Suppose that a and b are positive integers such that both

are irrational. For what values of a and b is

rational? Prove your answer.

(c) Again assuming a and b positive integers such that both

are irrational, for what values of a and b is

rational? Prove your answer.

Thank you. I'm stumped!

Let x=a and x=b be the roots of the equation x^2 - mx + 2 = 0.

Suppose that x=a+\frac 1b and x=b+\frac 1a are the roots of the equation x^2 - px + q = 0.

Determine the value of q.

1) Compute the sum

2) Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations:

3) Suppose p+q+r = 7 and p^2+q^2+r^2 = 9. Then, what is the average (arithmetic mean) of the three products pq, qr, and rp?

4) Find the largest four-digit value of t such that

is an integer.