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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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Arithmetic: In which the Principles of Operating by Numbers are Analytically ...

Daniel Adams - 1848 - 312 σελίδες
...required. Hence, RULE. Multiply the larger term by the ratio, and subtract the less term from the product, divide the remainder by the ratio less 1 ; the quotient will be the sum of the series. EXAMPLES FOR PRACTICE. 2. If the extremes be 4 and 131073, and the ratio 8, what is the sum of the...

Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ...

Jeremiah Day, James Bates Thomson - 1848 - 252 σελίδες
...term in the given series. 373. To find the sum of a geometrical series. Multiply the last term into -the ratio, from the product subtract the first term, and divide the remainder by the ratio less one. Obaer. From the above formula, in connexion with the one. iu Art. 368, there may be the same variety...

A Theoretical and Practical Treatise on Algebra ...

Horatio Nelson Robinson - 1848 - 320 σελίδες
...following rule for the sum of a geometrical series ; RULE. Multiply the last term by the ratio, and from the product subtract the first term, and divide the remainder by the ratio less one. EXAMPLES FOR THE APPLICATION OF EQUATIONS (1) AND (2). 1. Required the sum of 9 terms of the series,...

Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - 1848 - 240 σελίδες
...— — ^— = - =•. r — 1 i — l Hence, the RULE, FOR FINDING THE SUM OF A GEOMETRICAL SERIES. Multiply the last term by the ratio, from the product subtract the frst term, and divide the remainder by the ratio less one. EXAMPLES. 1. Find the sum of 10 terms of...

Daboll's Complete Schoolmaster's Assistant: Being a Plain Comprehensive ...

Nathan Daboll, David Austin Daboll - 1849 - 249 σελίδες
...last term, (or the extremes,) and the ratio given, to find the sum of the series. RULE. Multiply tke last term by the ratio ; from the product subtract...term, and divide the remainder by the ratio, less 1, and the quotient will be the sum of all the terms. EXAMPLES. 1 . A man bought 6 yards of cloth, giving...

ARITHMETIC ON THE PRODUCTIVE SYSTEM

ROSWELL C. SMITH - 1850
...when the extremes and ratio are given, to find the sum of the series, we have the following RULE. 21. Multiply the last term by the ratio, from the product...the quotient will be the sum of the series required. 22. If the extremes be 5 and 6,400, and the ratio 6, what is the whole amount of the series ? 5 r =...

The Speedy Calculator: Being a System of Arithmetic

Benjamin Naylor - 1850 - 324 σελίδες
...(2) (the first term of the first.) Hence the RULE. product will be the last or greater extreme 2- — multiply the last term by the ratio, from the product...first term, and divide the remainder by the ratio less one for the sum of the series, or raise the ratio to a power equal to the number of terms ; subtract...

A New System of Arithmetic on an Improved Plan

Charles Guilford Burnham - 1850
...find the sum of the series, we have the following l 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 betiveen the two extremes by the ratio less 1, and add the quotient...

An Elementary Treatise on Algebra: Designed as First Lessons in that Science

Horatio Nelson Robinson - 1850 - 240 σελίδες
...gives the following rule for the sum of a series. RULE . — Multiply the last term by the ratio, and from the product subtract the first term, and divide the remainder by the ratio less one. GENERAL EXAMPLES IN GEOMETRICAL PROGRESSION. 1. What is the ratio of the series 2, 6, 18, 54,...

Stoddard's Practical Arithmetic

John Fair Stoddard - 1852 - 299 σελίδες
...ii. ART. 197. Given the first term, the last term, and th« ratio, to find the sum of all the terms. RULE. Multiply the last term, by the. ratio ; from...first term, and divide the remainder by the ratio di minisked by one. 1 . The first term of a geometrical progression is 4, tha iast term is 62500, and...




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