Question

Write each sum using summation notation.
1+ 2 + 3 + 4 + ⋯ + 1000

Answer 1

`\sum_(k=1)^(1000) k`

Explanation:

You have to use the summation notation formula:

`\sum_(k)^(n) f(k) = f(1) + f(2) +...+f(n)`

where k is the starting number, n is the ending number and f(k) is the function or the expression to be added.

In this case, you have the sum of the integer numbers from 1 to 1000. Therefore, k=1 and n=1000.

Now, you have to obtain the function f(k) which is the representation of the expression needed to obtain the correct result of the sum.

f(k=1) = 1

f(k=2)=2

f(k=3)=3 ...

You can notice that the value of k corresponds to te value of f(k) therefore f(k) = k

Replacing the values of k, n and f(k) in the formula:

`\sum_(k=1)^(1000) k = 1+2+3+4+...+1000`