26 Summing geometric progressions

Transcript

The algebra of how sums of geometric progressions mightn’t be everyone’s thing.

Although the derivation of the formulas is difficult, the most important thing is to be able to identify sequences that arise as either being arithmetic or geometric (or neither) and then being able to correctly apply the formulas if the sum or n^th term is required.  This Scratch program will help you check your working.

Geometric progressions

What fraction of the square below is shaded black?  What if the pattern continues forever with smaller and smaller squares being drawn inside? Hints Still stuck?  More hints (warning, spoilers!)