Answer the following questions related to the sum of a constant sequence.
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Answer the following questions related to the sum of a constant sequence.
(i) Define a finite series and write the general sigma–notation form for the sum of the first n terms of a sequence a1,a2,…,an.
(ii) Starting from first principles (writing out all the terms explicitly), explain why k=1∑n1=n for every positive integer n.
(iii) Distinguish between the sums k=1∑n1 and k=1∑nk with respect to the type of sequence involved and the respective closed-form expressions for their sums.