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" Evidently the sum can be made to differ from 2 by as little as we please, by taking a sufficient number of terms. "
Secondary Algebra - Page 332
by George Egbert Fisher, Isaac Joachim Schwatt - 1900 - 442 pages
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...of the series 1 + e -f- i + 4 etc., is evidently less than 2; but by taking a great number of terms, the sum can be made to differ from 2 by as little as we please. Hence 2 is the limit of the sum of the series, when the number of the terms is increased indefinitely...
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...of the series 1 + í + } + i etc., is evidently less than 2; but by taking a great number of terms, the sum can be made to differ from 2 by as little as we please. Hence 2 is the limit of the sum of the series, when the number of the terms is increased indefinitely...
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1879 - 262 pages
...1 + i + J + £ etc., is evidently less than 2 ; but by taking a great number of terms, the sum caii be made to differ from 2 by as little as we please. Hence 2 is the limit of the sum of the series, when the number of the terms is increased indefinitely...
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A treatise on mathematics, as applied to the contructive arts

Francis Campin - 1882 - 412 pages
...i, i, &c. Here a =. 1, r = % ; therefore — ^ — = - = 2, and from 2 the sum can be made to differ as little as we please by taking a sufficient number of terms. The sum then of an infinite number of terms of this series will be 2, and 2 is the limit to which the...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 272 pages
...the sum of the series 1 + J + i + -g-, etc., is less than 2 ; but by taking a great number of terms, the sum can be made to differ from 2 by as little as we please. Hence 2 is the limit of the sum of the series, when the number of the terms is increased indefinitely...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...many terms of this series are taken, the sum can never equal 2; but by taking a great number of terms the sum can be made to differ from 2 by as little as we please. Hence we say that the limit of the sum of the series as the number of terms is indefinitly increased...
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Text-book of Algebra: With Exercises for Secondary Schools and Colleges, Part 1

George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1898 - 714 pages
...approaches the finite value 2 more and more nearly as more and more terms are included in the sum, and that the sum can be made to differ from 2 by as little...we please, by taking a sufficient number of terms. The exact sum 2, however, can never be obtained. This theory can be applied to find the value of a...
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New School Algebra

George Albert Wentworth - Algebra - 1898 - 520 pages
...the sum of the series 1 + ^ + £ + |, etc., is less than 2 ; but by taking a great number of terms, the sum can be made to differ from 2 by as little as we please. Hence, 2 is the limit of the sum of the series, when the number of the terms is increased indefinitely...
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New School Algebra

George Albert Wentworth - Algebra - 1898 - 428 pages
...the sum of the series 1 + ¿ + £ + \, etc., is less than 2 ; but by taking a great number of terms, the sum can be made to differ from 2 by as little as we please. Hence, 2 is the limit of the sum of the series, when the number of the terms is increased indefinitely...
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Elements of Algebra with Exercises

George Egbert Fisher, Isaac Joachim Schwatt - 1899 - 506 pages
...approaches the finite value 2 more and more nearly as more and more terms are included in the sum, and that the sum can be made to differ from 2 by as little...we please, by taking a sufficient number of terms. The exact sum 2, however, can never be obtained. Ex. 8. Verify that .6 = |. We have .666 ... = Д +...
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