SOLUTION: Find the rule for the mapping if R maps unto A 2 3 4 5 | | | | 1 3 6 10. Nb.R>1 and is a natural number. Thanks

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Question 1143563: Find the rule for the mapping if R maps unto A
2 3 4 5
| | | |
1 3 6 10.

Nb.R>1 and is a natural number. Thanks
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


(2(2-1))/2 = 2/2 = 1
(3(3-1))/2 = 6/2 = 3
(4(4-1))/2 = 12/2 = 6
(5(5-1))/2 = 20/2 = 10

The rule is

(n(n-1))/2
Answer by ikleyn(52805)   (Show Source): You can put this solution on YOUR website!
.

The rule  f(n) =    pointed by the tutor @greenestamps, is not a unique rule for this map.


There are INFINITELY MANY other rules that provide the same map.


For example, all the polynomials


    F(n) =  + m*(n-2)*(n-3)*(n-4)*(n-5)


with any constant real (or integer) coefficient "m" produce the same map.


Notice that the added polynomial  m*(n-2)*(n-3)*(n-4)*(n-5)  is equal to zero at all the points  {2, 3, 4, 5} on the number line.


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