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In this lesson, we will learn how to expand an expression written using sigma notation and how to use it to express the sum of a sequence of terms that follow a rule.

Q1:

Evaluate 6 ๐ = 2 ๏ โ 2 5 .

Q2:

Express the series โ 1 2 + 1 4 โ 1 8 + 1 1 6 โ โฏ in sigma notation ๏ .

Q3:

Expand and then evaluate 4 ๐ = 1 ๏ ( 3 1 ๐ + 8 0 ) .

Q4:

Evaluate 5 ๐ = 1 ๐ ๏ ๏ผ 1 2 ๏ .

Q5:

Evaluate ๏ซ ๏ ๏ฒ ๏ฉ ๏ โ 8 ๐ .

Q6:

Express the series 5 4 ร 1 2 + 5 4 ร 2 4 + 5 4 ร 3 6 + โฏ + 5 4 ร 2 4 0 in sigma notation.

Q7:

Expand and then evaluate ๐ ๐ = 1 ๏ 1 ๐ + 4 2 โ 1 ๐ + 4 1 .

Q8:

Evaluate 9 ๐ = 4 ๐ โ 1 ๏ 1 4 ( 2 ) .

Q9:

Evaluate 8 ๐ = 3 ๐ โ 1 ๏ 5 4 ( 2 ) .

Q10:

Expand and then evaluate 4 ๐ = 1 2 ๏ ๏น 1 9 ๐ ๏ .

Q11:

Evaluate 1 3 ๐ = 8 ๐ โ 1 ๏ ( 2 ) .

Q12:

A child wants to build a pyramid using identical wooden cubes. The pyramidโs apex consists of one cube, its second row consists of two cubes, and its third row consists of three cubes, and so on for five rows. Use the sigma notation to describe the amount of cubes needed to build the pyramid and then calculate this number.

Q13:

Expand and then evaluate ๏ช ๏ ๏ฒ ๏ง ๏ ๏ ( 2 โ 5 2 ) .

Q14:

Expand and then evaluate ๏ช ๏ ๏ฒ ๏ง ๏ ๏ ๏น ( โ 4 ) โ 5 2 ๏ .

Q15:

Express the series 8 + 3 2 + 7 2 + 1 2 8 + โฏ + 5 1 2 in sigma notation.

Q16:

Express the series ( 3 2 ร 3 3 ) + ( 3 3 ร 3 4 ) + ( 3 4 ร 3 5 ) + โฏ in sigma notation.

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