The question goes on about relationship of Lucas numbers and Fibonacci Numbers. In one of the question we determine a relationship that Sn=∑(i=1) to n of Li = 1+3+4+7+....+Ln=L(n+2) -3 with the L(n+2) - 3 part the determinent relationship. I have to prove using mathmatical induction that ∑(i=1) to n of Li = L(n+2) -3
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Took me a bit to decipher statement...
true for n = 1.....L1 = 1 = L3 - 3 = 4 - 3
assume for n = k....1 +3+4+....+ Lk = L(k+2) - 3
then add L(k+1) to both sides..left side correct..right side is L(k + 2) + L(k+1) - 3 = L(k+3) - 3
from the definition of L(k+3)
true for n = 1.....L1 = 1 = L3 - 3 = 4 - 3
assume for n = k....1 +3+4+....+ Lk = L(k+2) - 3
then add L(k+1) to both sides..left side correct..right side is L(k + 2) + L(k+1) - 3 = L(k+3) - 3
from the definition of L(k+3)