| Mathematics - 1801 - 444 pages
...ratio. PROBLEM I. Given the first termt the last term, and the ratio, to find tht sum of the series. **RULE.* Multiply the last term by the ratio, and from...term, and the remainder, divided by the ratio less** I, will give the sum of the series. EXAMPLES. * DEMONSTRATION. Take any series whatever, as i, 3, 9,... | |
| Samuel Webber - Arithmetic - 1812 - 260 pages
...ratio. PROBLEM 1. Given thefirst term, the last term, and the ratio, to find the sum of the series. **RULE.* Multiply the last term by the ratio, and from...term, and the remainder, divided by the ratio less** 1, will give the sum of the series. * DEMONSTRATION. Take any series whatever, as 1, 3, 9, 27, 81,... | |
| Nathan Daboll - Arithmetic - 1813 - 244 pages
...The first term, the last term (or the extremes) and the ratio given, to find the sum of the series **RULE. Multiply the last term by the ratio, and from the product subtract the first term** ; then divide the remainder by the ratio, less by 1, and the quotient will be the sum of all the terms.... | |
| Arithmetic - 1818 - 264 pages
...Given the first term, the last term, (or extremes') and the ra* t|O, to find the sum of the series, **RULE. Multiply the last term by the ratio, and from the product subtract the first term, and the** rem ainder, divided by the ratio less I, wjif'give the sum of all the terms of the series. EXAMPLES.... | |
| Phinehas Merrill - Mathematics - 1819 - 116 pages
...•Given the first term, the last term, and the ratio, to find the aggregate or total sum of the series. **RULE. — Multiply the last term by the ratio, and...divided by the ratio less one, will give the sum of the** whole series. EXAMPLES. 1. The first term of a series in geometrical progression is 1 , the last term... | |
| Zadock Thompson - Arithmetic - 1826 - 176 pages
...ratio. Problem I. The Jlnt term, the latt term, and the ratio given to find the turn of the series. **RULE.* — Multiply the last term by the ratio, and...term, and the remainder divided by the ratio, less** 1, will give the sum of the series. Examples. 1 . The first term of a series in geometrical progression... | |
| Daniel Parker - Arithmetic - 1828 - 358 pages
...stand over the first term, the number oí the exponents must equal the number of terms. PROBLEM I. # **RULE. Multiply the last term by the ratio, and from the product subtract the first term** ; then divide the remainder by the ratio less one, and the quotient will be the sum of all the terms.... | |
| William Kinne - 1829 - 246 pages
...ratio. PROBLEM 1. Given the first term, the last term, and the ratio, to find the sum of the series. **RULE. — Multiply the last term by the ratio, and...term, and the remainder divided by the ratio less** 1, will give the sum of the series. EXAMPLES. 1 . The extremes of a geometrical progression are 1 and... | |
| Nathan Daboll - Arithmetic - 1829 - 254 pages
...The first term, the last term (or the extremes) and the ratio given, to find the sum of the series. **RULE. Multiply the last term by the ratio, and from the product subtract the first term** ; then divide the remainder by the ratio, less by 1, and the quotient will be the sum of all the terms.... | |
| James L. Connolly (mathematician.) - Arithmetic - 1829 - 266 pages
...first term, the last term, or the extremes, and the ratio, given to find the sum of the series. RULK 1. **Multiply the last term by the ratio, and from the product subtract the first term;** then divide the remainder by the ratio less one, and the quotient will be the sum of all the terms.... | |
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