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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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## A manual of arithmetic

...of the given series, as the ratio less 1 is greater than 1. . , 3. Consequently, if we divide this remainder by the ratio less 1, the quotient will be the sum of the given series ; as will be manifest in the following example. Ex.—To find the sum of the series 5:15:...

## Elements of Algebra: Being an Abridgement of Day's Algebra Adapted to the ...

Jeremiah Day - 1844 - 252 σελίδες
...series. 373. To find the sum of a geometrical series. Multiply the last term into the ratio, from {he product subtract the first term, and divide the remainder by the ratio less one. Obter. From the above formula, in connexion with the one in Art. 368, there may be the same variety...

## The Teachers' Assistant: Or, A System of Practical Arithmetic ...

1845 - 198 σελίδες
...terms given, which, being multiplied by the first term, will give the last term, or greater extreme. 2. Multiply the last term by the ratio, from the product...subtract the first term, and divide the remainder by ratio less one for the sum of the series. EXAMPLES. 1. A thresher wrought 20 days, and received for...

## An Elementary Treatise on Algebra: Theoretical and Practical

Horatio Nelson Robinson - 1846 - 262 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 OP EQUATIONS (1) AND (2). 1. Required the sum of 9 terms of the series,...

## A Treatise on Algebra

Elias Loomis - 1846 - 346 σελίδες
...Hence, to find the sum of the terrns 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 a series is a decreasing one, andr consequently represents a fraction, it is convenient to...

## The Columbian Calculator; Being a Practical and Concise System of Decimal ...

Almon Ticknor - 1846 - 264 σελίδες
...is the last term, or greater extreme. . 2. Multiply the last term by the ratio, and from the prodiut subtract the first term, and divide the remainder by the ratio ^ less one ; the quotient will be the sum of the series. Or, raise the ratio to a power equal to the number...

## A Treatise on Algebra

Elias Loomis - 1846 - 346 σελίδες
...I already found, we obtain Ir — a ~ r — 1 ' PROGRESSIONS. Multiply the last term by the ratio, subtract the first term, and divide the remainder by the ratio less one. If a series is a decreasing one, and r consequently represents a fraction, it is convenient to...

## Practical and Mental Arithmetic on a New Plan: In which Mental Arithmetic is ...

Roswell Chamberlain Smith - 1847 - 282 σελίδες
...Wlien the Extremes and Ratio are given, to find the Sum of (he Series, we have tlie following easy RULE. Multiply the last term by the ratio, from the...quotient will be the sum of the series required. 9. If tbe extremes be 5 and 6400, and the ratio 6, what is the whole amount of tbe series 1 6400X6 — 5...

## The American Arithmetic

...rule in Art. 179, then multiply the last term by the ratio, subtract the first term from the product, and divide the remainder by the ratio, less 1 ; the quotient will be the sum of all the terms. 1. If the first term of a geometrical series be 2, and the ratio 3, what is the 4th...

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

Joseph Ray - 1848 - 240 σελίδες
...Therefore, *= =— = =•. r—1 r—l Hence, the 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. EXAMPLES. 1. Find the sum of 10 terms of the progression 2, 6, 18, 54, &,1:. The last term =2x39=2X19683=39366....