
1/50*51+1/51*52+1/52*53+1/53*54+1/54*55
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1/50*51+1/51*52+1/52*53+1/53*54+1/54*55
=(1/50-1/51)+(1/51-1/52)+(1/52-1/53)+(1/53-1/54)+(1/54-1/55)
=1/50-1/51+1/51-1/52+1/52-1/53+1/53-1/54+1/54-1/55
=1/50-1/55
=1/550
=(1/50-1/51)+(1/51-1/52)+(1/52-1/53)+(1/53-1/54)+(1/54-1/55)
=1/50-1/51+1/51-1/52+1/52-1/53+1/53-1/54+1/54-1/55
=1/50-1/55
=1/550
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