Simplify and evaluate the following constant sums.
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Simplify and evaluate the following constant sums.
(i) Find a simplified expression, in terms of m, for k=1∑m+57, where m is a positive integer.
(ii) Hence determine k=1∑m+57−k=1∑m−27 and express your answer in the simplest form in terms of m.
(iii) Using your result from part (ii), calculate the value of the expression when m=12.