## Featured resource

### Savannah Dreams

A delightful picture book, with a simple story about Savannah and her family as they go hunting in the bush. Over Sunday to Friday, the rest of the family discover lots of delicious bush tucker and count how many crabs or snakes or waterlily stems they have caught or collected, but Savannah finds only junk. That is until Sunday, when Savannah makes the greatest catch of all.

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# Grandi’s series

Consider 1 – 1 + 1 – 1 + ….

Is the answer 0, 1 or ½? Or all three?

Approaches:

[A]    (1 – 1) + (1 – 1) + (1 – 1) + … = 0 + 0 + 0 + … = 0

[B]     1 + (– 1 + 1) + (– 1 + 1 ) + (– 1 + 1) + … = 1 + 0 + 0 + 0 + … = 1

[C]     S = (1 – 1 + 1 – 1 + 1 – 1 +  …) , so

1 – S = 1 – (1 – 1 + 1 – 1 + 1 – 1 + …) = 1 – 1 + 1 – 1 + 1 – 1 + 1 … = S

1 – S = S

1 = 2S

S = ½