Where is the Fibonacci sequence in the Pascal triangle?

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

Count as follows.

Start left with a 1.

While on a number:

- Move right

- Move up

- Add to running total.

Let's go.

First row.

1.

Stop.

Second row.

1

Stop.

Third row.

1, right, up

1

Stop.

Fourth row

1, right, up

2

Stop.

Fifth row

1, right, up

3, right, up

1

Stop.

Sixth row

1, right, up

4, right, up

3

Stop.

Totals were 1, 1, 2, 3, 5, 8.

Fibonacci sequence, obvious.

Now what's the proof?

Grade 1 piano exam result

5 weeks ago

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