The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13...; starting with 0 and 1, each number is the sum of the two previous numbers.
The Lucas numbers follow the same rule, but start with 2 and 1: 2, 1, 3, 4, 7, 11, 18,...
What's the sum of the first k Lucas numbers?
What's the sum of the squares of the first k Lucas numbers?
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Submitted by Old Original Oskar!
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Rating: 2.0000 (5 votes)
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Solution:
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(Hide)
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The Lucas numbers are 2, 1, 3, 4, 7, 11, 18, 29, 47, 76... Calculating the sums gives 2, 3, 6, 10, 17, 28, 46, 75... and it's easy to guess that equals L(n+2)-1.
The squares are 4, 1, 9, 16, 49, 121, 324,
841, 2209, 5776... and the sums are 4, 5, 14, 30, 79, 200, 524, 1365, 3574... are L(n)L(n+1)+2. |
