Question 6
$$p$$ and $$p+1$$ are both prime numbers. Then the value of $$\frac{p(p+1)}{2p+1}$$ lies between
Solution
Two consecutive integers can both be prime only when they are $$2$$ and $$3$$, so $$p=2$$. The expression becomes $$\frac{2 \times 3}{5}=\frac{6}{5}$$. This lies between $$1$$ and $$\frac{7}{5}$$.
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