$$\int_{7}^{\infty}\frac{1}{\sqrt{v-5}}$$ I tried using the limit comparison test and found that $\frac{1}{\sqrt{v}}\leq\frac{1}{\sqrt{v-5}}$ and therefore tried t find $\lim_{x\to\infty}\frac{\frac{1}{\sqrt{v}}}{\frac{1}{\sqrt{v-5}}}$ and found that it converges as the limit is 1 . However, the answer is diverge . Am i doing it right ?
Should i have used the Direct Comparison Test instead or could the answer also be solved by using the limit comparison test? because i'm not quite sure when to use which one
Best Answer
You were almost there. Indeed, you forgot the last step:
$$\int_7^\infty\frac1{\sqrt v}dv\to\infty$$
Thus, it diverges.