I used Symbolab to confirm one of my solutions and realized something strange when solving this summation: image of question
Symbolab factors out the unneeded constant out of the equation, which is normal but then once the summation is solved, it only multiplies the first term in the summation's solution by the constant it factors out: Symbolab doing as described above I thought it was supposed to multiply every term like so: What i expected
How come in this question, only the first term is multiplied?
Symbolab has made an error.
The line $$ \frac{1}{n^2 -1} \cdot \frac{1}{3}n^3 + \frac{3}{2}n^2 + \frac{13}{6}n $$ should be $$ \frac{1}{n^2 -1} \cdot \left( \frac{1}{3}n^3 + \frac{3}{2}n^2 + \frac{13}{6}n \right) \text{,} $$ as you correctly noticed.