Answer:
[tex]f(20)=\frac{505}{2}[/tex]
Step-by-step explanation:
We want to find [tex]f(20)[/tex] where [tex]f(x)=\frac{1}{x}+\frac{2}{x}+\frac{3}{x}+\cdots+\frac{100}{x}[/tex]
[tex]f(20)=\frac{1}{20}+\frac{2}{20}+\frac{3}{20}+\cdots \frac{100}{20}[/tex]
[tex]f(20)=\frac{1}{20}(1+2+3+\cdots+100)[/tex]
We can use the following formula here:
[tex]1+2+3+\cdots+n=\frac{n(n+1)}{2}[/tex]
So since [tex]n=100[/tex] we have:
[tex]f(20)=\frac{1}{20}(\frac{100(100+1)}{2})[/tex]
[tex]f(20)=\frac{1}{20}(\frac{100(101)}{2})[/tex]
[tex]f(20)=\frac{1}{20}(50(101))[/tex]
[tex]f(20)=\frac{50}{20}(101)[/tex]
[tex]f(20)=\frac{5}{2}(101)[/tex]
[tex]f(20)=\frac{505}{2}[/tex]
