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The Transactions of the Royal Irish Academy (Volume 11 )

The Transactions of the Royal Irish Academy (Volume 11 )


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated.1810 Excerpt: ... th Demonstration.--The first differences of the y powers of the Binomials are derived by taking away the first members th of those powers, for this is to subduct the powers of the next lesser Binomials. The second differences of the y powers of the Binomials (or the differences of the first differences) will be equal to the sums of the separate differences of the separate members of the first differences, which members being the powers of terms in an arithmcical series, the indices of which powers are y--I, --2, 3, &c. the first differences of these will be known from the first differences of the y powere: For, if j---q+=ydq + Cdqr +&c. then willpr l--qr = 1--)dqr 2+Cd'qr 3-f-&c.; and/)'--% qr =(_2)rf?r J+Cdq + &C. J But there are wanting none except the highest members of the expressions for the first differences, in order to obtain the highest members of the expressions for the second differences, th and none except the highest members of the n-1 differences th in order to obtain the highest members of the - differences, for the differences of the highest members contain higher powers than the differences of the lower members. Since then, the highest members of the first differences th of the j powers are yd multiplied by the powers of numbers bers in arithmetical progression, whose Index is --1, and th since the highest members of those --1 powers are (TM--1) d multiplied by powers whose index is TM--2. Therefore the highest members of the second differences will be the common multiplier d. (TM--l)d multiplied by powers whose Index i --2. Again the highest members of the differences of the --2 powers of numbers in arithmetical progression are (--2)d. multiplied by the powers whose Index is--3). Therefore the highest mem...


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Product Details
  • ISBN-13: 9781235807480
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Height: 246 mm
  • No of Pages: 134
  • Spine Width: 7 mm
  • Width: 189 mm
  • ISBN-10: 1235807487
  • Publisher Date: 01 Feb 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 254 gr

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