Question

If $f(x) - f(y) = ln\bigg(\frac{x}{y}\bigg) +x-y$, then find** ** $\sum^{20}_{k=1}f'\bigg(\frac{1}{k^2}\bigg)$

• A. 2890
• B. 2390
• C. 1245
• D. None of this

Answer 1

Answer: (A)

2890

Answer 2

The correct option is (A): $2890$

$f(x)-In(x)-x=f(y)-In\, y-y$

$=f(x)-In(x)-x=c$

$=f(x)=c+x+In \,x$

f"(x)=0+1+$\frac{1}{x}$

After simplification we get:

$20+\frac{20\times21\times41}{6}$

$20+2870=2890$