_{R.H.S =} [(No. of terms in L.H.S) × (No. + 1) × (2 × No. + 1)]

(i) 1² + 2² + 3² + 4² + …… + 10² = [10 (10 + 1) × (2 × 10 + 1)]

= [2310]

_{= 385}

_{(ii) 5}² + 6² +….. + 12² = 1² + 2² + ….. 12² – (1² + 2² + 3³ + 4²)

= [12 × (12 + 1) × (2 × 12 + 1)] - [4 ×(4 + 1) × (2 × 4 + 1)]

_{= 650 – 30}

_{= 620}