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

Rohan Mcpherson

Rohan Mcpherson

Answered question

2022-10-06

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

Answer & Explanation

Joel Reese

Joel Reese

Beginner2022-10-07Added 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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