Elementary Illustrations of the Differential And Integral Calculus
Elementary Illustrations of the Differential And Integral Calculus
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In our eReader you can find the full English version of the book. Read Elementary Illustrations of the Differential And Integral Calculus Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Elementary Illustrations of the Differential And Integral Calculus
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Again, every term of (1), except the first, being greater than a, and the terms being m-\-2 in number, (m -|- 2)0 is less than the sum of the terms in (1). Consequently, (m -L- 2) A . . Sum of terms in (2) T - ~ is greater than the ratio - -f - : ^, (m -f 2)# sum of terms in (1) since its numerator is greater than the last numerator, and its denominator less than the last denominator. But Il8 ELEMENTARY ILLUSTRATIONS OF A (m + 2)a ~a which is independent of m, and is a finite quantity. Hence th...e ratio of the sums of the terms is always finite, whatever may be the number of terms, at least unless the terms in (2) increase without limit.
As the number of interposed values increases, the interval or difference between them diminishes ; if, therefore, we multiply this difference by the sum of the values, or form T \(pa -j-
To quickly assess the difficulty of the text, read a short excerpt:
Again, every term of (1), except the first, being greater than a, and the terms being m-\-2 in number, (m -|- 2)0 is less than the sum of the terms in (1). Consequently, (m -L- 2) A . . Sum of terms in (2) T - ~ is greater than the ratio - -f - : ^, (m -f 2)# sum of terms in (1) since its numerator is greater than the last numerator, and its denominator less than the last denominator. But Il8 ELEMENTARY ILLUSTRATIONS OF A (m + 2)a ~a which is independent of m, and is a finite quantity. Hence th...e ratio of the sums of the terms is always finite, whatever may be the number of terms, at least unless the terms in (2) increase without limit.
As the number of interposed values increases, the interval or difference between them diminishes ; if, therefore, we multiply this difference by the sum of the values, or form T \(pa -j-
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