Can someone show a step-by-step process for simplifying the summation to $i \cdot n - i + 1$ as shown:
$\sum _{j=i}^{i \cdot n} 1 = i\cdot n - i + 1$
I don't know how to begin to solve this.
Can someone show a step-by-step process for simplifying the summation to $i \cdot n - i + 1$ as shown:
$\sum _{j=i}^{i \cdot n} 1 = i\cdot n - i + 1$
I don't know how to begin to solve this.
We are adding up $in-i+1$ terms, all equal to $1$. What happens when we add $47$ $1$'s together?
It is easy to make an error and be off by $1$. For example, what is $\sum_{j=2}^6 1$? We have a term of $1$ for each of $j=2,3,4,5,6$. The number of terms is not $6-2$, it is $6-2+1$.