 | Paul Deighan - 1804 - 504 σελίδες
...difference. n — i Number of terms. si Number of the feries. Prop. I. In any Arithmetkal feries, the fum of the extremes multiplied by the number of terms is equal to double the fum of the terms, »'. e. a-|-j»Xn=2/ or «a+/it=a/. Dntonllration. a +5 *+* a+3e a+$e... | |
 | Thomas Taylor - 1823 - 168 σελίδες
...series I +2 + 3+4+5, &c., when the number of terms is even and finite, the sum of the two middle terms, multiplied by the number of terms, is equal to twice the sum of the series. Thus in four terms, 3 + 2 =: 5 and 5 X 4 = 20, which is the double of 10, the sum of the... | |
 | Emerson Elbridge White - 1870 - 350 σελίδες
...An inspection of the above shows that the sum of the first and last terms of an arithmetical series, multiplied by the number of terms, is equal to twice the sum of all the terms. Hence, The sum of all the terms of an arithmetical series is equal to the product of one half the sum... | |
 | Emerson Elbridge White - 1883 - 374 σελίδες
...An inspection of the above shows that the sum of the first and last terms of an arithmetical series, multiplied by the number of terms, is equal to twice the sum of all the terms. Hence, 5. The sum of all the terms of an arithmetical series is equal to the product of one half the... | |
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An inspection of the above shows that the sum of the first and last terms of an arithmetical series, multiplied by the number of terms, is equal to twice the sum of all the terms. 