[(1)/(4)] + [(1)/(4) + (1)/(200) ] + [ (...

`[(1)/(4)] + [(1)/(4) + (1)/(200) ] + [ (1)/(4) + (1)/(100)] + [ (1)/(4) + (1)/(200)] + ..... + [ (1)/(4) +(199)/(200) ] ` ,
where [x] denotes the greatest integer `le` x, is equal to :

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The give expression can be written as
`[1/4]+[1/4+1/200]+[1/4+2/200]+[1/4+3/200]`
`+….+[1/4+199/200]`
`=[200.1/4]=[50]=50` [from property (xiv)]

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