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Similar Sequence Sum! (Posted on 2004-10-07) Difficulty: 3 of 5
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?

See The Solution Submitted by Old Original Oskar!    
Rating: 2.0000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts some numbers | Comment 2 of 6 |
For comparison with formulae:
 n     L(n) Sum(L(n)) Sum((L(n))^2)
1 2 2 4



2 1 3 5
3      3      6         14
 4      4     10         30
 5      7     17         79
 6     11     28        200
 7     18     46        524
 8     29     75       1365
 9     47    122       3574
10     76    198       9350
11    123    321      24479
12    199    520      64080
13    322    842     167764
14    521   1363     439205
15    843   2206    1149854
16   1364   3570    3010350
17   2207   5777    7881199
18   3571   9348   20633240
19   5778  15126   54018524
20   9349  24475  141422325
21  15127  39602  370248454
22  24476  64078  969323030

  Posted by Charlie on 2004-10-07 13:11:42
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