Let be the sum of the first terms of the sequence 0, 1, 1, 2, 2, 3, 3, where the th term
Chapter 9, Problem 104(choose chapter or problem)
Let f(n) be the sum of the first n terms of the sequence 0, 1, 1,2, 2, 3, 3, 4,. . ., where the nth term is given by
\(a_{n}=\left\{\begin{array}{cl}n / 2, & \text { if } n \text { is even } \\(n-1) / 2, & \text { if } n \text { is odd }\end{array}\right.\)
Show that if x and y are positive integers and x > y then xy= f(x + y) - f(x - y).
Text Transcription:
a_n={n/2, if n is even
(n-1)/2, if n is odd
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