(a) Find the generating function for the sequences (i) 0, 1,0, 0, 0, ... ; (ii) 0, 1, 1,1,1,... ; (iii) 0, 1, 2, 3, 4, . . .;
(iv) 0, 1, 3, 6, 10, ....
(b) Use result (iv) from part (a) to find a formula for ∑nk=1 k.