Question

F(x)=(1/x)+(2/x)+(3/x)+(4/x)...(100/x) what is f(20)

Answer 1

Answer:

$f(20)=\frac{505}{2}$

Step-by-step explanation:

We want to find $f(20)$ where $f(x)=\frac{1}{x}+\frac{2}{x}+\frac{3}{x}+\cdots+\frac{100}{x}$

$f(20)=\frac{1}{20}+\frac{2}{20}+\frac{3}{20}+\cdots \frac{100}{20}$

$f(20)=\frac{1}{20}(1+2+3+\cdots+100)$

We can use the following formula here:

$1+2+3+\cdots+n=\frac{n(n+1)}{2}$

So since $n=100$ we have:

$f(20)=\frac{1}{20}(\frac{100(100+1)}{2})$

$f(20)=\frac{1}{20}(\frac{100(101)}{2})$

$f(20)=\frac{1}{20}(50(101))$

$f(20)=\frac{50}{20}(101)$

$f(20)=\frac{5}{2}(101)$

$f(20)=\frac{505}{2}$