Hello, yc6489!

Sorry, I don't understand the question . . .

Prove for , where are Lucas numbers.

But that is thedefinitionof Lucas Numbers.

. . where

So what is there to prove?

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It's similar to saying:

"Prove that is the Harmonic Series."

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Fibonacci started with 1 and 1.

Lucas started with 1 and 2 ... and gets into the history books.

Okay . . .

. . . . . . . for

We have the sequence: .

. . which are the lesser-known Soroban numbers.