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Question

The sum of the fractions 12+16+112+120+130+142+156+172+190+1110+1132 is


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Solution

The sum of the fractions 12+16+112+120+130+142+156+172+190+1110+1132

Simplify the fraction as follow:

12+16+112+120+130+142+156+172+190+1110+1132=(1−12)+(12−13)+(13−14)+(14−15)+(15−16)+(16−17)+(17−18)+(18−19)+(19−110)+(110−111)+(111−112)⇒12+16+112+120+130+142+156+172+190+1110+1132=(1−112)⇒12+16+112+120+130+142+156+172+190+1110+1132=1110Hence, the sum of the fractions 12+16+112+120+130+142+156+172+190+1110+1132 is 1110.


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