Mastering Mathematics Smartly
by Wee Wen Shih

A unique self-help website that provides comprehensive coverage of mathematics at A-level & beyond, written in a student-friendly style.

Method of differences

A typical problem involves these steps:

(1)  Break up a general term into parts, usually through the use of partial fractions or trigonometric identity.

(2)  Cancel terms systematically, leaving only some behind. Typically, you are left with either:

  • top-right and bottom-left terms, or
  • top-left and bottom-right terms.

(3)  Determine whether the resulting sum converges. The usual approach is to determine the value of each term in the expression as n approaches infinity. For example, the term 1/(n + 1) approaches 0 as n approaches infinity.

Try this!

Relationship with summation of series

This is an interesting question provided by a forumer:

Suggested approach:

P.S. It is a useful strategy because many terms cancel out (just like the case of method of differences) when we add the equations up.