           20           20
Suppose that Σ aₖ = 0 and Σ bₖ = 7. Find the value of
           k = 1          k = 1

  20
a. Σ 3aₖ
  k = 1

검증된 단계별 안내

Identify the given information: \( \sum_{k=1}^{20} a_k = 0 \) and \( \sum_{k=1}^{20} b_k = 7 \).

Focus on the expression to find: \( \sum_{k=1}^{20} 3a_k \). Notice that the summation is over \( 3a_k \), which means each term \( a_k \) is multiplied by 3.

Use the property of summations that allows constants to be factored out: \( \sum_{k=1}^{n} c \cdot x_k = c \sum_{k=1}^{n} x_k \). Applying this, we get \( \sum_{k=1}^{20} 3a_k = 3 \sum_{k=1}^{20} a_k \).

Substitute the known value of \( \sum_{k=1}^{20} a_k = 0 \) into the expression: \( 3 \times 0 \).

Conclude that the value of \( \sum_{k=1}^{20} 3a_k \) is \( 3 \times 0 \), which simplifies to 0.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Summation Notation (Sigma Notation)

Summation notation uses the Greek letter sigma (Σ) to represent the sum of a sequence of terms indexed by an integer variable. Understanding how to interpret and manipulate these sums is essential for evaluating expressions involving series, such as Σ aₖ or Σ 3aₖ.

Properties of Summations

Summations have linearity properties, meaning constants can be factored out and sums can be split or combined. For example, Σ c·aₖ = c·Σ aₖ, which allows simplification of expressions like Σ 3aₖ by factoring out the constant 3.

Given Series Values and Their Use

Knowing the values of given sums, such as Σ aₖ = 0 and Σ bₖ = 7, is crucial for solving problems. These values can be substituted directly into expressions to find unknown sums or simplify calculations.

20 20Suppose that Σ aₖ = 0 and Σ bₖ = 7. Find the value of k = 1 k = 1 20a. Σ 3aₖ k = 1

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Summation Notation (Sigma Notation)

Properties of Summations

Given Series Values and Their Use

20 20
Suppose that Σ aₖ = 0 and Σ bₖ = 7. Find the value of
k = 1 k = 1

20
a. Σ 3aₖ
k = 1