Series (Grade 12 NSC Matric Mathematics): Quizzes

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What is a series?

The sum of terms in a sequence

What symbol represents the sum of the first nn terms of a sequence?

SnS_n

For which condition does a geometric series have a sum to infinity?

∣r∣<1|r| < 1

In sigma notation ∑i=mnTi\sum_{i=m}^{n} T_i, where is the lower bound mm shown?

Below the sigma symbol

How many terms are in the series ∑i=37Ti\sum_{i=3}^{7} T_i?

55

What does ∑i=1n(ai+bi)\sum_{i=1}^{n} (a_i + b_i) equal?

∑i=1nai+∑i=1nbi\sum_{i=1}^{n} a_i + \sum_{i=1}^{n} b_i

For constant cc, what does ∑i=1n(c⋅ai)\sum_{i=1}^{n} (c \cdot a_i) equal?

c⋅∑i=1naic \cdot \sum_{i=1}^{n} a_i

What is the formula for the sum of an arithmetic series?

Sn=n2(2a+(n−1)d)S_n = \frac{n}{2}(2a + (n-1)d)

What is the formula for the sum of a finite geometric series?

Sn=a1−rn1−rS_n = a \frac{1 - r^n}{1 - r}

What is the formula for the sum to infinity of a geometric series when ∣r∣<1|r| < 1?

S∞=a1−rS_∞ = \frac{a}{1 - r}

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