A Course of Mathematics in Two Volumes Composed And More Especially Designed
A Course of Mathematics in Two Volumes Composed And More Especially Designed
Charles Hutton
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Find the cube root of -— ^ — ■ — ;7n in an infinite ferles. Anf. -—X ( 1 — -— T + r r* &C4 * . Cix 1 1 . Find the value of — ^ -, in an infinite feries. a~ — ax -{- . V . . X ^2 ^4 x^ ^ Ani. — + o r - -^> &c. a or a> a^ ARITHMETICAL PROPORTION. Arithmetical Proportion is the relation which two quantities, of the fame kind, bear to each otlier, in refped; to their difference. Four quantities are faid to be in Arithmetical Proportion, when the difference between the firft and feCond is equal to t...he difference between the third and fourth. Thus, 3, 7, 12, 16, and a^ a -{- h, c, c -^ b, are arith- metically proportional. Arithmetical Progrefiion is when a feries of quantities cither increale or decreafe by the iame common difference. Thus, 1, 3, 5, 7, 9, 11, S^c, and a, a -{- b, a + 2b, a + 3^, a -\- 4:bf a -\-bb, &:c, are feries in arithmetical progrefiion, whofe common differences arc 2 and b. The moft ufeful part of arithm. Etical proportion is con- tained in the following theorems : 1 .
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