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Prove that the number of partitions of the positive integer n into parts each of which is at most 2 equals ? n/2 ? + 1. (Remark: There is a formula, namely the nearest integer to (n+3)²/12 , for the number of partitions of n into parts each of which is at most 3 but it is much more difficult to prove. There is also one for partitions with no part more than 4, but it is even more complicated and difficult to prove.)

Name: Prove that the number of partitions of the positive integer n into parts each of which is at most 2 equals ? n/2 ? + 1. (Remark: There is a formula, namely the nearest integer to (n+3)²/12 , for the number of partitions of n into parts each of which is at most 3 but it is much more difficult to prove. There is also one for partitions with no part more than 4, but it is even more complicated and difficult to prove.)
Uploaded: 2022-03-20T05:01:55-08:00
Duration: 3 min 3 s
Channel: Krishna G

          Prove that the number of partitions of the positive integer n into parts each of which is at most 2 equals ? n/2 ? + 1. (Remark: There is a formula, namely the nearest integer to (n+3)²/12 , for the number of partitions of n into parts each of which is at most 3 but it is much more difficult to prove. There is also one for partitions with no part more than 4, but it is even more complicated and difficult to prove.)

Prove that the number of partitions of the positive integer n into parts each of which is at most 2 equals ? n/2 ? + 1. (Remark: There is a formula, namely the nearest integer to (n+3)²/12 , for the number of partitions of n into parts each of which is at most 3 but it is much more difficult to prove. There is also one for partitions with no part more than 4, but it is even more complicated and difficult to prove.)

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Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Krishna G

03/20/2022

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Prove that the number of partitions of the positive integer n into parts each of which is at most 2 equals ⌊ n/2 ⌋ + 1. (Remark: There is a formula, namely the nearest integer to (n+3)^2/12, for the number of partitions of n into parts each of which is at most 3 but it is much more difficult to prove. There is also one for partitions with no part more than 4, but it is even more complicated and difficult to prove.)