Write a recursive formula for the sequence 1, 2, 3/2, 4/6, 5/24...

Rohan Mcpherson 2022-10-06 Answered
Write a recursive formula for the sequence 1, 2, 3/2, 4/6, 5/24...
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Answers (1)

Joel Reese
Answered 2022-10-07 Author has 17 answers
A direct formula would be:
a n = n ( n - 1 ) !
So we find:
a n + 1 a n = ( n + 1 n ! ) ÷ ( n ( n - 1 ) ! ) = ( n + 1 ) ( n - 1 ) ! n n ! = n + 1 n 2
Hence:
a n + 1 = n + 1 n 2 a n
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