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Question

The value of the expression [1027]+[1127]+[1227]+...+[3527] is

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Solution

[1027]+[1127]+[1227]+...+[3527]=[927+127]+[927+227]++[927+2627]=[13+127]+[13+227]++[13+2627]

We know that,
[x]+[x+1n]+[x+2n]++[x+n1n]=[nx][x+1n]+[x+2n]++[x+n1n]=[nx][x]
So,
[13+127]+[13+227]++[13+2627]=[27×13][13]=[9]0=9

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