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What are reciprocals?

What are reciprocals? Here are some definitions.

Noun
  1. plural of reciprocal
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The mean obtained by taking the reciprocal of the arithmetic mean of the reciprocals of a set of non-zero numbers.
The question was to determine the exact value of the convergent infinite series obtained by summing the reciprocals of the squares of the positive integers.
Our clients include many of the largest national and global insurers, reinsurers and reciprocals in Canada.
They drew up multiplication tables and tables of reciprocals, squares, cubes and exponentials, and used them to calculate compound interest and mortgage repayments.
These tables also assisted in division, for the values that head them were all reciprocals of regular numbers.
Those jurisdictions enacting legislation relating to the Plan have provided for exemptions for e.g. reinsurers, farm mutuals, and reciprocals.

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