BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Drupal: Date iCal//NONSGML kigkonsult.se iCalcreator 2.18// METHOD:PUBLISH X-WR-CALNAME;VALUE=TEXT:Calendar of Events BEGIN:VTIMEZONE TZID:America/New_York BEGIN:STANDARD DTSTART:20261101T020000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:EST END:STANDARD BEGIN:DAYLIGHT DTSTART:20270314T020000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:EDT END:DAYLIGHT END:VTIMEZONE BEGIN:VEVENT UID:calendar.71072.field_date.0@calendar.lafayette.edu DTSTAMP:20260606T111253Z DESCRIPTION:Normal\n0\nfalse\nfalse\nfalse\nEN-US\nX-NONE\nX-NONE\n\nDefSem iHidden='false' DefQFormat='false' DefPriority='99'\nLatentStyleCount='376 '>\nUnhideWhenUsed='true' QFormat='true' Name='heading 2'/>\nUnhideWhenUse d='true' QFormat='true' Name='heading 3'/>\nUnhideWhenUsed='true' QFormat= 'true' Name='heading 4'/>\nUnhideWhenUsed='true' QFormat='true' Name='head ing 5'/>\nUnhideWhenUsed='true' QFormat='true' Name='heading 6'/>\nUnhideW henUsed='true' QFormat='true' Name='heading 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font-family:'Calibri'\,sans-serif\;\n mso-ascii-font -family:Calibri\;\n mso-ascii-theme-font:minor-latin\;\n mso-hansi-font-fami ly:Calibri\;\n mso-hansi-theme-font:minor-latin\;\n mso-bidi-font-family:'Ti mes New Roman'\;\n mso-bidi-theme-font:minor-bidi\;}\n\n*Abstract: For a po sitive integer d\, let p_d(n) := 0^d + 1^d + … + n^d\; \ni.e.\, p_d(n) is the sum of the first d-th powers up to n. It’s well known \nthat p_d(n) is a polynomial of degree d+1 in n. While this is usually proved \nby induct ion\, once d is not small it’s a challenge as one needs to know the \npoly nomial for the inductive step. In this talk\, we show how this difficulty \ncan be bypassed by giving a simple proof that p_d(n) is a polynomial of \ndegree d+1 in n by using L’Hopital’s rule\, and show how we can then \nd etermine the coefficients by Cramer’s rule. *\n\n \n\n  DTSTART;TZID=America/New_York:20260430T121500 DTEND;TZID=America/New_York:20260430T131000 LAST-MODIFIED:20260424T135647Z LOCATION:Pardee 217 SUMMARY:MAAD talk - Sums of Powers by L'Hopital's Rule URL;TYPE=URI:https://calendar.lafayette.edu/node/71072 END:VEVENT END:VCALENDAR