Question

1/2.5+1/5.8+1/8.11+.......+1/(3n-1)(3n+2)=n/6n+4
proved this sum quickly please.​

Answer 1

tₙ = 1/(3n–1)(3n+2)

So, Sₙ = Σ₁ⁿ (tₙ)

Now, using Vₙ – Vₙ-₁ method

Sₙ = 1/3(1-2) [1/(3n+2) – 1/2]

Sₙ = 1/3 [3n/6n+4]

∴ Sₙ = n/6n+4