Ok 2 questions which I can't solve.
1. Given that the summation of U(r) between n and r=1 is 1/2 n^2 (n^2 -1), show that U(n) = 2n^3 - 3n^2 + n. Henc express summation of r^3 between n and r =1 in terms of n. [the restults for summation of r^2 and r between n and r=1 may be assumed]
2. Given that the geometric progression, whose 1st 2 terms are a and b (a,b are non-zero), has a sum to infinity of (a+4b), find the value of summation of (b/a)^r between r=1 and infinity.
Answer is 3.
Thanks!
Hi,
For Q1, use the fact that T_n = S_n - S_{n - 1}, where T_n = U_n and S_n = 1/2 n^2 (n^2 -1). Then, take the summation of both sides of the equation U_n = 2n^3 - 3n^2 + n.
For Q2, notice that b/a represents common ratio. Now, a / (1 - b/a) = a + 4b. Find the value of b/a.
Thanks.
Cheers,
Wen Shih