Sequences & Series Flashcards

1
Q

Arithmetic sequence formula

A

Un = a + (n-1)d

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2
Q

Arithmetic series formulas

A

Sn = n/2 (2a + (n-1)d) OR Sn = n/2(a+L)

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3
Q

How to work out arithmetic series formula

A

Write out terms a + (a+d) + (a+2d) + … + (a+(n-1)d)
Write out terms reversed
(a+(n-1)d) + … + (a+2d) + (a+d) + a
Add them: 2Sn = n(2a + (n-1)d)
Divide by 2: Sn = n/2(2a+(n-1)d)

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4
Q

Geometric sequence formula

A

Un = ar^n-1

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5
Q

Geometric series formula

A

Sn = a(1-r^n) / 1-r OR Sn = a(r^n -1) / r-1

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6
Q

How to work out geometric series formula

A

Sn = a + ar + ar^2 … ar^n-2 + ar^n-1
make another and times by r, then minus rSn from Sn
Sn - rSn = a - ar^n
Take out common factor:
Sn (1-r) = a(1-r^n)
divide by 1-r: Sn = a(1-r^n) / 1-r

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7
Q

What is sum to infinity

A

S = a / 1-r

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8
Q

What does divergent series mean

A

terms of series are getting larger

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9
Q

What does convergent series mean

A

terms of series are getting smaller

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10
Q

How to know if series is convergent

A

if |r| < 1

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