Question

Write the following sums in sigma notation (i.e. using the symbol P): 7+12+17+22+27+32; 1+1+1+1+1; 3 4 5 6 7 3+6+12+24; 1+ 21 + 31 + 14 + 51 + 16; 1+2+3+4; 1+1+5+ 7 +...(atotalof10elements). 2 3 4 5 9 27 x+2x2 +3x3 +4x4 +5x5; 1−2q+3q2 −4q3 +5q4 −6q5 +7q6

Answer 1

Відповідь:

Пояснення:

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Answer 2

Summation Notation (Sigma Notation)

In mathematics, sigma notation (Σ) is used to represent the sum of a series of terms. The general form of sigma notation is:

Σ (expression) from (starting index) to (ending index)

Let's write the given sums in sigma notation:

1. 7 + 12 + 17 + 22 + 27 + 32 This sum has a common difference of 5 between consecutive terms. We can express it in sigma notation as: Σ (7 + 5n) from n = 0 to 5

2. 1 + 1 + 1 + 1 + 1 This sum has a constant value of 1 for each term. We can express it in sigma notation as: Σ (1) from n = 0 to 4

3. 3 + 4 + 5 + 6 + 7 + 3 + 6 + 12 + 24 This sum does not have a constant difference or value for each term. We can express it in sigma notation as: Σ (a_n) from n = 0 to 8 Here, a_n represents the nth term of the given sequence.

4. 1 + 21 + 31 + 14 + 51 + 16 This sum does not have a constant difference or value for each term. We can express it in sigma notation as: Σ (a_n) from n = 0 to 5 Here, a_n represents the nth term of the given sequence.

5. 1 + 2 + 3 + 4 This sum has a constant difference of 1 between consecutive terms. We can express it in sigma notation as: Σ (n) from n = 1 to 4

6. 1 + 1 + 5 + 7 + ... (a total of 10 elements) This sum does not have a constant difference or value for each term. We can express it in sigma notation as: Σ (a_n) from n = 0 to 9 Here, a_n represents the nth term of the given sequence.

7. 2 + 3 + 4 + 5 + 9 + 27 + x + 2x^2 + 3x^3 + 4x^4 + 5x^5 This sum involves both constants and variables. We can express it in sigma notation as: Σ (a_n) from n = 0 to 10 Here, a_n represents the nth term of the given sequence, where: - a_0 = 2 - a_1 = 3 - a_2 = 4 - a_3 = 5 - a_4 = 9 - a_5 = 27 - a_6 = x - a_7 = 2x^2 - a_8 = 3x^3 - a_9 = 4x^4 - a_10 = 5x^5

8. 1 - 2q + 3q^2 - 4q^3 + 5q^4 - 6q^5 + 7q^6 This sum involves both constants and variables. We can express it in sigma notation as: Σ (a_n) from n = 0 to 6 Here, a_n represents the nth term of the given sequence, where: - a_0 = 1 - a_1 = -2q - a_2 = 3q^2 - a_3 = -4q^3 - a_4 = 5q^4 - a_5 = -6q^5 - a_6 = 7q^6

It's important to note that the choice of the starting and ending indexes in sigma notation can vary depending on the context and the specific series being represented.