chitr:Pm1234 Cauchy.svg

mool faail(SVG faail, saadhaaranat: 570 × 570 peeksels, faailaka aakaar: 27 KB)

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jaankaari
English: 1 − 2 + 3 − 4 + · · · as the Cauchy product of two copies of 1 − 1 + 1 − 1 + · · ·.

The illustration uses the rectangle metaphor for multiplication. One copy of 1 − 1 + 1 − 1 + · · · is depicted at the top, another at the left. A black length or area represents a positive quantity; a red length or area represents a negative quantity. Multiplying two line segments results in a rectangle whose color is determined by the law for multiplying signed numbers:

1 * 1 = 1
−1 * 1 = −1
1 * −1 = −1
−1 * −1 = 1
The double series resulting from the multiplication of the two single series is expressed as a single series using the Cauchy product rule. Each term of the resulting series is a combination of terms from the double series running from south-west to north-east. The result is identified as 1 − 2 + 3 − 4 + · · ·.
dinaank 2007-03-04
srot User created
lekhak user:Melchoir
anya sanskaranon

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This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Generic, 2.0 Generic and 1.0 Generic license.
tum mukt ho:
  • saajha karein – rachana ko kaupi, vitrit aur sanchaarit karne ke liye
  • reemiks karne ke liye – kaam anukoolit karne ke liye
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vartamaan 12:14, 14 April 2007 12:14, 14 अप्रैल 2007 के संस्करण का अंगूठाकार प्रारूप। 570 × 570 (27 KB) Ysangkok Saving as plain SVG in Inkscape.
03:55, 4 March 2007 03:55, 4 मार्च 2007 के संस्करण का अंगूठाकार प्रारूप। 570 × 570 (41 KB) Melchoir add border
03:52, 4 March 2007 03:52, 4 मार्च 2007 के संस्करण का अंगूठाकार प्रारूप। 550 × 550 (41 KB) Melchoir 1 − 2 + 3 − 4 + · · · as the Cauchy product of two copies of 1 − 1 + 1 − 1 + · · ·

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