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 Βιβλία Βιβλία 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
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο ## Practical Arithmetic, by Induction and Analysis

Joseph Ray - 1857 - 320 σελίδες
...for Case II. — Multiply the greatest term by the ratio ; from the product subtract the leasttcrm, and divide the remainder by the ratio less 1 ; the quotient will be 'the sum of the series. NOTE. — When a series is decreasing, and the number of terms infinite, the last term is naught. In... ## Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Μέρος 2

Joseph Ray - 1857 - 396 σελίδες
...— 1 ' — 1 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... ## Adams's Improved Arithmetic: Arithmetic, in which are Combined the Analytic ...

Daniel Adams - 1861 - 280 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. EXAOTPLES. 2. If the extremes be 4 and 131072, and the ratio 8, what is the sum of the series ? Ans.... ## The Elements of Algebra: Designed for Beginners

Elias Loomis - 1862 - 281 σελίδες
...terms of a geometrical progression, we have the following RULE. Multiply the last term by the ratio, subtract the first term, and divide the remainder by the ratio less one. Examples. 1. What is the sum of nine terms of the series 1, 3, 9, 27, 81, etc. ? We have already... ## New Elementary Algebra: in which the First Principles of Analysis are ...

Benjamin Greenleaf - 1863 - 324 σελίδες
...value of ar" in (4), S — rl — a. r-4 '-7^1 . <•'•) Hence the RULE. die last term by the ratio, subtract the first term, and divide the remainder by the ratio less 1. NOTE. If the last term is not given, it may be found by Case I. ; or, formula (4) may be used instead... ## Elements of Algebra: For Colleges, Schools, and Private Students, Βιβλίο 2

Joseph Ray - 1866 - 406 σελίδες
...— a Therefore ...... 8= - =- = - =-. Hence, Rule for finding the Sum of a Geometrical Series. — Multiply the last term by the ratio, from the product...first term, and divide the remainder by the ratio less one. Find the sum of 6 terms of the progression 3, 12, 48, etc. 3=4095, Ans. order that both terms... ## New Elementary Algebra: Containing the Rudiments of Science for Schools and ...

Horatio Nelson Robinson - 1866 - 312 σελίδες
...— 1)8 = rL — a. Or, 8 = ^. « Hence, the following 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 PRACTICE. 1. The first term is 5, the last term 1280, and the ratio 4 ; what is the... ## Eaton's Elementary Algebra: Designed for the Use of High Schools and Academies

William Frothingham Bradbury - 1868 - 252 σελίδες
......... -f' + Zr(2) Subtracting (1) from (2), rS — S = I r — a lr _ a Whence, S= - — . Hence, RULE. ' Multiply the last term by the ratio, from...first term, and divide the remainder by the ratio less one. 1. Given a = 2, I= 20000, and r = 10, to find S. lr — a _ 20000 X 10 — 2 _ gf>p . S — -jr--r... ## Practical Arithmetic, by Induction and Analysis, Βιβλίο 3

Joseph Ray - 1857 - 320 σελίδες
...Role for Case II. — Multiply the greatest term by the ratio ; from the product subtract the least term, and divide the remainder by the ratio less 1 ; the quotient will be the sum of the series. NOTE. — When a series is decreasing, and the number of terms infinite, the last term is naught. In... ## Eaton's Elementary Algebra: Designed for the Use of High Schools and Academies

William Frothingham Bradbury - 1868 - 252 σελίδες
...-{- -|-Z-|-Zr (3) Subtracting (1) from (2), r S — S = / r — a Whence, S = — -p. Hence, T ^~~~ 1 RULE. Multiply the last term by the ratio, from the product subtract the first term, and divide tlie remainder by the ratio less one. 1. Given a = 2, 1= 20000, and r = 10, to find S. *=£=£ = soooo^io...