There are 'n'people and there are 'n²' marbles on the whole. No two people collect the same number of marbles.Each of them collects at least one marble.FIND THE MAXIMUM NUMBER OF MARBLES ANY ONE OF THEM CAN COLLECT.

let first peson gets minimum marble = 1

second gets  minimum 2 marbles , third gets minimum 3 marbles & so on.......

this is an AP series whose first term is 1 & common difference is 1 ...

now total marbles distributed  to n-1 people = k

k = [(n-1)/2][2+(n-2)] = n(n-1)/2

now , last person gets all remaining marbles ..

remaining marbles = total - distributed

                          = n² - (n(n-1)/2)

                          = n(n+1)/2

this is the maximum number of marble which any 1 of them can get ...

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