 | Warren Colburn - Algebra - 1825 - 400 pages
...,,Adding these term to term as they stand, But it has just been shown that a + l = b + k — c + i &ic. That is, all the terms are now equal, and one of them...whole number of terms will give the whole sum : thus if Hence, the sum of a series of numbers in progression by difference is one half the product of the... | |
 | Warren Colburn - Algebra - 1826 - 290 pages
...n. Adding these term to term as they stand, But it has just been shown that a + l = b + k = c + i, &c. That is, all the terms are now equal, and one...number of terms by the sum of the first and last terms. Example. How many strokes does the hammer of a clock strike in 12 hours ? a = 1, I = 12, and n = 12.... | |
 | Warren Colburn - Algebra - 1828 - 288 pages
...= l + k + i +h + ____ d+c Adding these term to term as they stand, But it has just been shown that That is, all the terms are now equal, and one of them...number of terms by the sum of the first and last terms. Example. How many strokes does the hammer of a clock strike in 12 hours ? «=l, 1= 12, and M i= 12.... | |
 | Warren Colburn - Algebra - 1828 - 292 pages
...of them being multiplied by the whole number of terms will give the whole sum ; thus 2 S = n (a + l) Hence, the sum of a series of numbers in progression...number of terms by the sum of the first and last terms. Example. How many strokes does the hammer of a clock strike in 12 hours ? «=l, 1=12, and » = 12.... | |
 | Warren Colburn - Algebra - 1830 - 288 pages
...a. Adding these term to term as they stand, But it has just been shown that a-\-l = b-\-k = c-\-i, &c. That is, all the terms are now equal, and one...half of the product of the number of terms by the mm of thejirst and last terms. Example. How many strokes does the hammer of a clock strike in 12 hours... | |
 | Warren Colburn - Algebra - 1838 - 282 pages
...Adding these term to term as they stand, But it has just been shown that f ',j a + l = b-\-k = c + i, &c. That is, all the terms are now equal, and one...Hence, the sum of a series of numbers in progression by differ- . .-» ence is one half of the product of the number of terms by the sum of the, first and... | |
 | Warren Colburn - Algebra - 1839 - 308 pages
...a. Adding these term to term as they stand, But it has just been shown that a-\-l = b-\-k = c-\-i, &,c. That is, all the terms are now equal, and one...whole number of terms will give the whole sum : thus .«-.'n(o"+*) 2 Hence, the sum of a series of numbers in, progression by difference is one half of... | |
 | Warren Colburn - Algebra - 1844 - 280 pages
...+ a. Adding these term to term as they stand, But it has just been shown that a-}-l = b-\-k=;c-\-i, &c. That is, all the terms are now equal, and one...number of terms by the sum of the first and last terms. Example. How many strokes does the hammer of a clock strike in 12 hours ? a=l, I = 12, and n = 12.... | |
 | Warren Colburn - Algebra - 1844 - 280 pages
...term to term as they stand, /ZS=(a+0 + (8+i) + <c + 0 + (rf + *) + " But it has just been shown that That is, all the terms are now equal, and one of them...number of terms by the sum of the first and last terms. Example. How many strokes does the hammer of a clock strike in 12 hours ? a — 1, I= 12, and n = 12.... | |
 | Thomas H. Palmer - Arithmetic - 1854 - 356 pages
...Progression by Differences ? IL The sum of all the terms in a Progression by Differences, is equal to half the product of the number of terms by the sum of the first and last terms. Exercises for the Slate or Slack-board. 1. What is the sum of a progression by differences, whose first... | |
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Hence, the sum of a series of numbers in progression by difference is one half of the product of the number of terms by the sum of the first and last terms. Example. How many strokes does the hammer of a clock strike in 12 hours ? a — 1, I= 12, and... 
