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" Hence, to find the sum, multiply the first term by the difference between unity and that power of the ratio whose exponent is equal to the number of terms, and divide the product by the difference between unity and the ratio. Examples in Geometrical Progression. "
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... - Page 196
by Benjamin Peirce - 1860 - 284 pages
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A New and Complete System of Arithmetick: Composed for the Use of the ...

Nicolas Pike - Algebra - 1808 - 470 pages
...the other extreme. RULE — Multiply, or divide, (as the case may require) the given extreme by such power of the ratio, whose exponent* is equal to the number of terms lefs J, and the produdl or quotient, will be the other extreme. EXAMPLES. ever, as 2. 6. 18. 54. 162....
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1837 - 300 pages
...— S = arn — a, or (r — 1) S= ar» — a = a(rn — 1); whence a r» — aa (rn — 1) r — 1 " r — 1 Hence, to find the sum, multiply the first...and the ratio. Examples in Geometrical Progression. 186. Corollary. The two equations • (r—l)S = a(r»— 1) give the means of determining either two...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1837 - 300 pages
...— a, or (r — I) S= ar*— a = a (r» — 1); - .. , -<•: .. whence arn — aa r» — 1 8 — Hence, to find the sum, multiply the first term by...and the ratio. Examples in Geometrical Progression. 186. Corollary. The two equations I = ar»-1 give the means of determining either two of the quantities...
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The National Arithmetic, on the Inductive System: Combining the Analytic and ...

Benjamin Greenleaf - Arithmetic - 1839 - 356 pages
...terms, to find the other extreme. RULE. If the series be ascending, multiply the given extreme by such power of the ratio, whose exponent is equal to the number of * This rule cannot well be demonstrated except by Algebra SECT. L vI.] GEOMETRICAL SERIES. 213 terms...
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Higher Arithmetic: Designed for the Use of High Schools, Academies, and Colleges

George Roberts Perkins - Arithmetic - 1841 - 274 pages
...the terms, repeated as many times as there are units in the number of terms, less one, equal to the power of the ratio whose exponent is equal to the number of terms, diminished by one and multiplied by the first term. Hence, when we have given the first term, the ratio,...
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The National Arithmetic ...: Combining the Analytic and Synthetic Methods ...

Benjamin Greenleaf - Arithmetic - 1841 - 334 pages
...terms, to find the other extreme. RULE. If the series be ascending, multiply the given extreine by such power of the ratio, whose exponent is equal to the number of * Thii rule cannot well be demonstrated except by Algebra terms lesp 1 ; and the product will be the...
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An Elementary Arithmetic ...: Serving as an Introduction to the Higher ...

George Roberts Perkins - Arithmetic - 1846 - 266 pages
...the terms, repeated as many times as there are units in the number of terms, less one, equal to the power of the ratio whose exponent is equal to the number of terms, diminished by one, and multiplied by the first term. Hence, when we have given the first term, the...
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Higher Arithmetic: Designed for the Use of High Schools, Academies, and ...

George Roberts Perkins - Arithmetic - 1849 - 344 pages
...1398101 pecks. Case III. Since by Case I. the last term is equal to the first term multiplied into a power of the ratio whose exponent is equal to the number of terms, less one, it follows that the first term is equal to the last term divided by the power of the ratio...
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Higher Arithmetic: Designed for the Use of High Schools, Academies, and ...

George Roberts Perkins - Arithmetic - 1850 - 356 pages
...the terms, repeated as many times as there are units in the number of terms, less one, equal to the power of the ratio, whose exponent is equal to the number of terms diminished by one, and multiplied by the first term. Hence, when we have given the first term, the...
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An Elementary Treatise on Algebra

Benjamin Peirce - Algebra - 1851 - 294 pages
...n, or (r — 1) 8 = ar n — a = a (r n — 1) ; whence o = - = —. a r" — an(r n — 1) r — 1 r — 1 Hence, to find the sum, multiply the first...Geometrical Progression. 260. Corollary. The two equations (r — l}S = a(r" — 1) give the means of determining either two of the quantities a, I, r, n, and...
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