F6 ASGS!!

1. for the series (1) + (2+3) + (4+5+6) + (7+8+9+10) + ....., find
(a)the number of terms in the nth bracket
(b)the total number of terms in the first n brackets
(c)the sum of the terms in the first n brackets
(d)the sum of the terms in the nth bracket

2. fot the series (1) + (2+2^2) + (2^3 + 2^4 +2^5) +....., find
(a)the first term and the last term in the nth bracket
(b)the sum of all the terms in the nth bracket
(c)the sum of all the terms in the first n brackets

3. given that S(1) = a + ar +ar^2 + ..... + ar^(n-1) and S(2) = a^2 + a^2 r^2 + a^2 r^4 +....+ a^2 r^2(n-1), show that (r+1)S(2) = (r-1)S(1)^2 + 2aS(1).

4. if the sum to infinity of the G.S. T(1), T(2), T(3).... is 21 abd the sum of all the odd terms T(1) , T(3), T(5),.....is 63/4, find the first term and the common ratio of the sequence.

5. Consider the G.S. 1, 1/k, 1/(k+2),...........
(a) find the possible value(s) of k.
(b) for each value of k found in (a), determine whether the sum to infinity of the sequence.

6. Suppose T(1), T(2), T(3),.... is a G.S. it is given that T(5)=48 and T(8)=6.
(a) find the first term and the common ratio
(b) find the sum to infinity of the sequence.
(c) consider another sequence T(1), (1/2)T(2), (1/2)^2 T(3), (1/2)^3 T(4),....
(i) show that the sequence is a G.S.
(ii)find the sum to infinity of the sequence.