pure maths what to remember

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8 Terms

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periodic sequence

terms repeat in a cycle for k order (times) (e.g. -3,1,-3,1,-3… is periodic with order 2)

2
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arithmetic series

  1. Sn = n/2[2a + (n-1)d]

  2. Sn = n/2(a+l)

3
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arithmetic series proof

  1. write out normal sum Sn= a + (a+d) + (a+2d)+…+(a+(n-2)d)+(a+(n-1)d), [1], and reverse, [2]

  2. add [1] and [2]

4
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geometric sequences

Un = ar^(n-1)

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geometric series proof

  1. Sn = a + ar + ar² + … + ar^(n-1)

  2. multiply sum by r, rSn = ar + ar² + ar³ + … + ar^n

  3. subtract [1] and [2], Sn - rSn = a-ar^n

  4. Hence Sn(1-r) = a(1-r^n) and Sn = (a(1-r^n))/1-r

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7
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convergent geometric sequence condition

|r| < 1

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