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" Multiply the last term by the ratio, from the product subtract the first term, and divide the remainder by the ratio, less 1; the quotient will be the sum of the series required. "
Practical and Mental Arithmetic ... - Σελίδα 263
των Roswell Chamberlain Smith - 1839
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Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

Joseph Ray - 1852 - 396 σελίδες
...have +ar"~'+ar". This formula gives the following RULE, FOR FINDING THE SUM OF A GEOMETRICAL SERIES. Multiply the last term by the ratio, from the product subtract the first term,and divide the remainder by the ratio.less one. Ex. Find the sum of 6 terms of the progression...

Practical and Mental Arithmetic on a New Plan

Roswell Chamberlain Smith - 1852
...Series, we have the following easy RULE. Mnltiply the last term by the ratio, from the prodnct snbtract the first term, and divide the remainder by the ratio, less 1 ; the qnotient will be the snm of the series reqnired. 9. If the extremes be 5 and 6400, and the ratio 6,...

The New Federal Calculator, Or Scholar's Assistant

Thomas Tucker Smiley - 1854
...last term. 1. Raise the ratio to the power whose index is one less than the number of terms given. 3. Multiply the last term by the ratio; from the product...term, and divide the remainder by the ratio, less 1, for the sum of the series. Questions. What is Geometrical Progression? What is the ratio ? By what...

Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - 1854
...О rl- a r- 1 (1), and this formula, expressed in words, furnishes the following rule :— BULE. — Multiply the last term by the ratio ; from the product...first term, and divide the remainder by the ratio minus 1. This rule applies, of course, whether the ratio be whole or fractional, positive or negative....

A compendious course of mathematics, theoretical and practical

John Radford Young - 1855
...expressed in words, is the rule following, namely : — RULE. Multiply the last term by the common ratio ; from the product subtract the first term, and divide the remainder by the latio minus 1. The last term is the first multiplied as often by the ratio as there are terms following...

A Treatise on Algebra

Elias Loomis - 1855 - 316 σελίδες
...Hence, to find the sum of the terms of a geometrical progression, Multiply the last term by the ratio, subtract the first term, and divide the remainder by the ratio less one. If the series is a decreasing one, and r consequently represents a fraction, it is convenient...

The American Philosophical Arithmetic: Designed for the Use of Advanced ...

John Fair Stoddard - 1856 - 292 σελίδες
...ratio times 32 — 2. Therefore, the sum of the series equals 4 times 32 — 2-f-(4 — 1.) Hence, Multiply the last term by the ratio ; from the product...subtract the first term and divide the remainder by the raii^ diminished by one, and it will give the sum of all the terms. _ • 2. A gentleman engaged a...

Arithmetic on the Productive System: Accompanied by a Key and Cubical Blocks

Roswell Chamberlain Smith - 1856 - 311 σελίδες
...series, we have the following RULE. 21. Multiply the last term by the ratio, from the product subtrac the first term, and divide the remainder by the ratio, less 1 ; the qua tient will be the sum of the series required. 22. If the extremes be 5 and 6,400, and the ratio...

A New System of Arithmetic, on an Improved Plan, Embracing the Rules of ...

Charles Guilford Burnham - 1857
...find the sum of the series, we have the following RULES. I. Multiply the last term by the ratio, and from the product subtract the first term, and divide...remainder by the ratio less 1; the quotient will be the answer. II. Divide the difference between the two extremes by the ratio less 1, and add the quotient...

A NEW SYSTEM OF ARITHMETIC

CHARLES G. BURNHAM - 1857
...find the sum of the series, we have the following RULES. I. Multiply the last term by the ratio, and from the product subtract the first term, and divide...remainder by the ratio less 1; the quotient will be the answer. II. Divide the difference between the two extremes by the ratio less 1, and add the quotient...




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