VTMO 2026 - Grade 7 - Semifinal - SET 1 - Self-study Question 6

Question 6

For a positive integer $n$, let $T=\frac1{2\times5}+\frac1{5\times8}+\cdots+\frac1{(3n-1)(3n+2)}$. Which expression below is the simplified form of $T$?

Question illustration

$\frac{3n}{2(3n+2)}$
$\frac{n}{3n+2}$
$\frac{n}{2(3n+2)}$
$\frac{3n}{2(2n+3)}$
$\frac{3n}{2(n+3)}$