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x-1-1-1-x-n-1-m-x-n-m-m-x-n-m-1-nx-n-m-1-x-2-2-




Question Number 8740 by 123456 last updated on 25/Oct/16
x_(1,1) =1  x_(n+1,m) =x_(n,m) +m  x_(n,m+1) =nx_(n,m) −1  x_(2,2) =?
$${x}_{\mathrm{1},\mathrm{1}} =\mathrm{1} \\ $$$${x}_{{n}+\mathrm{1},{m}} ={x}_{{n},{m}} +{m} \\ $$$${x}_{{n},{m}+\mathrm{1}} ={nx}_{{n},{m}} −\mathrm{1} \\ $$$${x}_{\mathrm{2},\mathrm{2}} =? \\ $$
Commented by Yozzias last updated on 25/Oct/16
x_(2,1) =x_(1,1) +1=1+1=2  x_(2,2) =2x_(2,1) −1=2×2−1=3
$$\mathrm{x}_{\mathrm{2},\mathrm{1}} =\mathrm{x}_{\mathrm{1},\mathrm{1}} +\mathrm{1}=\mathrm{1}+\mathrm{1}=\mathrm{2} \\ $$$$\mathrm{x}_{\mathrm{2},\mathrm{2}} =\mathrm{2x}_{\mathrm{2},\mathrm{1}} −\mathrm{1}=\mathrm{2}×\mathrm{2}−\mathrm{1}=\mathrm{3} \\ $$
Commented by prakash jain last updated on 25/Oct/16
General formula for x_(n,m) ?
$$\mathrm{General}\:\mathrm{formula}\:\mathrm{for}\:{x}_{{n},{m}} ? \\ $$

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