SOLUTION: A partition of a natural number n is a representation of n as a sum of natural numbers in which order does not matter.3+2+2+1+1 is a partition of nine, as is 2+1+3+2+1 is also the

Algebra ->  Expressions-with-variables -> SOLUTION: A partition of a natural number n is a representation of n as a sum of natural numbers in which order does not matter.3+2+2+1+1 is a partition of nine, as is 2+1+3+2+1 is also the       Log On


   

Question 1127116: A partition of a natural number n is a representation of n as a sum of natural numbers in which order does not matter.3+2+2+1+1 is a partition of nine, as is 2+1+3+2+1 is also the same partition of 9. A number is also considered to be a partition of itself. If p(n) means the number of partitions of n, then what is the value of p(1)+p(2)+p(3)+p(4)+p(5)+p(6)+p(7)+p(8)?
Answer by MathLover1(20855) About Me  (Show Source):
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p%281%29-p%280%29=+0,.......................................+p%281%29+=+1
p%282%29-p%281%29-p%280%29=+0,................................+p%282%29+=+2
p%283%29-p%282%29-p%281%29=+0,................................+p%283%29+=+3
p%284%29-p%283%29-p%282%29=+0,................................ p%284%29+=+5
p%285%29-p%284%29-p%283%29%2Bp%280%29=+0,...........................p%285%29+=+7
p%286%29-p%285%29-p%284%29%2Bp%281%29=+0,...........................p%286%29+=+11
p%287%29-p%286%29-p%285%29%2Bp%282%29%2Bp%280%29=+0,......................p%287%29+=+15
p%288%29-p%287%29-p%286%29%2Bp%283%29%2Bp%281%29=+0,......................p%288%29+=+22