Answer:
[tex]b. \quad k^2 + k[/tex]
Step-by-step explanation:
For any summation of f(x) from 1 to k+1 we have
[tex]\displaystyle\sum_{k=1}^{k+1}f(x) = \displaystyle\sum_{k=1}^{k}f(x) + f(k+1)[/tex]
So the term to be added is [tex]f(k + 1)[/tex]
The expression is x² - x
Factoring [tex]x^2 - x[/tex] gives [tex]x(x - 1)[/tex]
For [tex]x = k + 1[/tex], the expression becomes :
[tex](k + 1)(k + 1 -1)\\= (k + 1)k\\= k^2 + k[/tex]
Answer: [tex]k^2 + k[/tex]
Option b
