Theorem 5. Abel's Lemma, or Partial Summation Given Sn ai + a2 + + an ... (a) a1v1+...+anVn = 81(v1 – V2)+...+8n-1(Vn-1– Vn)+SnVn (b) If m

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Theorem 5. Abel's Lemma, or Partial Summation<br>Given Sn<br>ai + a2 +<br>+ an<br>...<br>(a) a1v1+...+anVn = 81(v1 – V2)+...+8n-1(Vn-1– Vn)+SnVn<br>(b) If m < ai+<br>decreasing, then mvi < a¡v1 +<br>(c) If in (b) |sn|< M Vn, then |a1v1 + ... + an Vn| < Mv1 Vn.<br>|<br>... + an < M Vn, and v, is positive and<br>... + a„Vn < Mv1.<br>

Extracted text: Theorem 5. Abel's Lemma, or Partial Summation Given Sn ai + a2 + + an ... (a) a1v1+...+anVn = 81(v1 – V2)+...+8n-1(Vn-1– Vn)+SnVn (b) If m < ai+="" decreasing,="" then="" mvi="">< a¡v1="" +="" (c)="" if="" in="" (b)="">< m="" vn,="" then="" |a1v1="" +="" ...="" +="" an="" vn|="">< mv1="" vn.="" |="" ...="" +="" an="">< m="" vn,="" and="" v,="" is="" positive="" and="" ...="" +="" a„vn=""><>

Jun 04, 2022

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Theorem 5. Abel's Lemma, or Partial Summation Given Sn ai + a2 + + an ... (a) a1v1+...+anVn = 81(v1 – V2)+...+8n-1(Vn-1– Vn)+SnVn (b) If m

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