Question

Which of the following is equivalent to 5 k =0 a k in the picture?

Answer 1

A) a₀ +a₁ +a₂ +a₃ +a₄ +a₅

Explanation:

You want to know the meaning of ...

`\displaystyle \sum_(k=0)^5{a_k}`

Summation symbol

The summation symbol is the capital Greek letter sigma, Σ, the 18th letter of the Greek alphabet. Its subscript and superscript expressions generally tell you the name and range of an index variable.

The index variable will be found in the expression that is the argument of the summation symbol. The symbol is indicating the sum of the argument expressions for the different values of the index variable.

Application

Here, the argument expression is ...

`a_k`

The subscript expression k=0 on the Σ symbol tells you that "k" is the index variable, and the first item in the list being summed is a₀, the argument with k=0. Almost always, the index variable increases by 1 to obtain the next item in the sum. That means the next item in the sum is a₁.

The value of the index variable (k) keeps increasing by 1 until the limit specified in the Σ symbol superscript is reached. Here, that value is 5. This means the last item in the sum is a₅.

The meaning of the symbol is ...

`\boxed{\displaystyle \sum_(k=0)^5{a_k}=a_0+a_1+a_2+a_3+a_4+a_5}`