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Τρίτη 16 Νοεμβρίου 2021

Problem of the Week - Just Sum Numbers

Kaori writes a sequence with the property that after the first two terms in the sequence, each term is equal to one more than the term before it, minus the term before that. In other words, tn=1+tn1tn2, for n3, where tn denotes the n th term in the sequence. 
The first term in Kaori’s sequence is x and the second term is y, where x and y are real numbers. That is, t1=x and t2=y. Determine the sum of the first 2021 terms in her sequence, as an expression in terms of x and y.
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