Find the sum of the series: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9

Sum of an arithmetic series can be easily calculated using the formula of the summation of n terms of the series.

Answer: The sum of the series 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 is equal to 45.

Let us go through the explanation to understand better.

Explanation:

Given series: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9

Since every position of the series is equal to the term of that series, the nth term of the series is T_n = n.

Sum of the series = ∑ T_n =  ∑ n

∑ n = n × (n + 1)/2 (Because sum of n natural numbers = n(n+1)/2)

∑ n = 9 × (9 + 1)/2 (Since total number of terms = n = 9)

∑ n = 9 × 10/2

∑ n = 9 × 5

∑ n = 45

For further series calculations, we can make use of the arithmetic series calculator.

Thus, the sum of the series is equal to 45.