Question

write the series using summation notation. then find the sum of the series.
1 + 2 + 3 + 4 + ... +15
\sum_{i=1}^{15} \square
the sum is \square.

Explanation:

Step1: Define summation notation

The series is the sum of integers from 1 to 15, so the summand is $i$.
Summation notation: $\sum_{i=1}^{15} i$

Step2: Apply arithmetic series sum formula

Use the formula for the sum of first $n$ integers: $\frac{n(n+1)}{2}$, where $n=15$.
Expression: $\frac{15(15+1)}{2}$

Step3: Calculate the sum

Simplify the expression.
Expression: $\frac{15 \times 16}{2} = 15 \times 8 = 120$

Answer:

Summation notation: $\sum_{i=1}^{15} i$
The sum is $120$