chitr:Pm1234 Cauchy.svg

mool faail ‎(SVG faail, saadhaaranat: 570 × 570 peeksels, faailaka aakaar: 27 KB)
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varnan[sampaadan]

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

PNG version

laaisensing[sampaadan]

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head is dastaavej ko Free Software Foundation dvaara prakaashit jee॰aaena॰aayoo fri daukyoomeinteshan license ke sanskaran 1.2 ya nae (bina kisi inveriyeint anubhaagon aur agale ya pichhle aavaran ke paath ke) ke antargat kaupi, vitrit evam/athva parivrtit karne ki anumati pradaan ki jaati hai. is license ki ek prati jee॰aaena॰aayoo fri daukyoomeinteshan license naamak anubhaag mein shaamil hai.
w:en:Creative Commons
एट्रीब्यूसन शेआर एलाइक 		yeh faail laaiseinsd hain is antargat kriyetiv kaumans etreebyooshan-share elaaik 3.0 anaported laaiseins .
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This licensing tag was added to this file as part of the GFDL licensing update.

w:en:Creative Commons
एट्रीब्यूसन शेआर एलाइक 		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
nimnalikhit kaaranon ke antargat:
  • etreebyoosan – aapko rachana ka shreya laaiseinsakarta athva lekhak ke bataaye gaye maadhyam se dena hoga (parantu is prakaar naheen ki usase lage ki ve aapko athva aapke dvaara rachana ke prayog ka samarthan karte hain).
  • sheaar elaaik – yadi aap is rachana mein koi parivartan athva badlaav karte hain ya ispar aadhaarit kuchh rachit karte hain to aap nishkarsh svaroop bani rachana ko keval isi ya iske saamaan kisi license ke antargat vitrit kar sakte hain.
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faail ka itihaas

faailaka puraana avataran dekhne ke liye dinaank/samay par klik karein.

dinaank/samay angoothaakaar praaroop aakaar sadasya pratikriya
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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