A Lesson in Pure Mathematics Contributed from Malaysia
From Rosalind Hoe Swee Yoke
I love teaching Pure Math. When I taught the "sum to infinity" of the convergent geometric progression ...1 + 1/2 + 1/4 + 1/8 + 1/16, I tried to demonstrate why, in the limit, it would approach a value of 2.

To help my students learn this, I held up 2 pieces of A4 paper.
Then I gave 1 piece to a sporting student named Teong Eng and said, "One plus..."
Then I folded and carefully tore the other piece into half and gave it to him…and said, "plus a half"
Then I folded and carefully tore the remaining half into half again, gave it to him and said "plus a quarter"...
......and I continued until there was hardly any paper in my hands.

Finally I asked the class… "How many pieces of paper does Teong Eng now have in his hand?"

Immediately they responded, "Two!"

I proceeded to use the formula ...Sum to infinity equals ... first term divided by one minus the common ratio.

It was a fun way to help my class of eleventh graders learn "Sum To Infinity".

Rosalind Hoe Swee Yoke is Head of the Mathematics Department at the Chung Hwa Confucian National Type High School in Penang, West Malaysia. She has taught at the school for 18 years.

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