IB_Mathematics_HL_Revision

IB_Mathematics_HL_Revision - Rahul Chacko IB Mathematics HL...

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Rahul Chacko IB Mathematics HL Revision – Step One Chapter 1.1 – Arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series. Sigma notation. Arithmetic Sequences Definition: An arithmetic sequence is a sequence in which each term differs from the previous one by the same fixed number: { u n } is arithmetic if and only if d u u n n 1 . Information Booklet d n u u n 1 1 Proof/Derivation: d u u n n 1 d u u n n 1 dn u u n 1 1 dn u u n 1 d n u u n 1 1 Derivations: d n u u n 1 1 1 1 n u u d n 1 1 d u u n n Information Booklet n n u u n d n u n S 1 1 2 1 2 2 Proof: S n = u 1 + u 2 + u 3 + …+ u n = u 1 + ( u 1 + d ) + ( u 1 + 2 d ) + ( u 1 + 3 d ) + …+ ( u 1 + ( n 1) d ) = u n + ( u n d ) + ( u n 2 d ) + ( u n + 3 d ) + …+ ( u n ( n 1) d ) 2 S n = n ( u 1 + u n ) n n u u n S 1 2 Derivations
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