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4 votes
4 votes
An organism is born on day K=1 with 1 cell. During day K=2,3,...... the organism produces $\frac{K^{2}}{K-1}$ times more new cells than it produced on day K-1. Number of cells in the organism at the end of 9th day if no cell dies is ___________

My Issue: Unable to solve the recurrence relation.

1 Answer

1 votes
1 votes

as given in question T(k)=(k2/k-1)*T(k-1)
T(1)=1
T(2)=(22/2-1)*T(1)=4
T(3)=(32/3-1)*T(2)=18
T(4)=(42/4-1)*T(3)=96  or  T(4)=42/3 * 32/2 * 22/1*1=1*2*3*4*4=4!*4=96
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T(k)=1*2*3*..........(k-1) *k2
T(k)=k! * k
 

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