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  • Perplex
    IB Math AAHL
    /
    Sequences & Series
    /

    Problem Bank

    [Maximum mark: 9]

    Consider a geometric sequence with first term ​u1​​ and common ratio ​r.

    1. Show that ​i=1∑n​(ui​+ui+1​)2=r−1u12​(r2n−1)(r+1)​​

      [5]
    2. Hence find the value of ​112+1102+11002+...+110000002. Give your answer in the form ​ba​(10c−d), where ​a,b,c,d∈Z.

      [4]

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