Discussion

Question:

If T_n = n² + n + 1, then find the sum of first 10 terms of this series.

Explanation:

Given, T_n = n² + n + 1

T₁ = 1² + 1 + 1
T₁ = 2² + 2 + 1
T₁ = 3² + 3 + 1
...
T₁₀ = 10² + 10 + 1

⇒ S₁₀ = (1² + 2² + 3² + ... + 10²) + (1 + 2 + 3 + ... + 10) + (1 + 1 + 1 + ... + 1)

⇒ S₁₀ = 10 × 11 × 21 / 6 + 10 × 11 / 2 + 10

⇒ S₁₀ = 385 + 55 + 10 = 450

Hence, 450.

» Your doubt will be displayed only after approval.

Doubts