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junior college 2 | H2 Maths
2 Answers Below
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Need help asap, the prove part is difficult.
Date Posted: 6 years ago
Views: 373
S(2n-1) = sum to first (2n-1) terms.
S(2n+1) = sum to first (2n+1) terms
= Sum to first (2n-1) terms + T(2n) + T(2n + 1)
So, S(2n +1) - S(2n - 1) = T(2n) + T(2n + 1)
It's given that T(n) = (-1)ⁿ n²
So S(2n +1) - S(2n - 1)
= T(2n) + T(2n + 1)
= (-1)²ⁿ x (2n)² + (-1)^(2n+1) x (2n +1)²
= ((-1)²)ⁿ x (4n²) + (-1)¹ x ((-1)²)ⁿ x (4n² + 4n + 1)
= 1ⁿ x 4n² - 1 x 1ⁿ x (4n² + 4n + 1)
= 4n² - 4n² - 4n - 1 (realise that 1ⁿ just = 1)
= - 4n - 1 (proved)
S(2n+1) = sum to first (2n+1) terms
= Sum to first (2n-1) terms + T(2n) + T(2n + 1)
So, S(2n +1) - S(2n - 1) = T(2n) + T(2n + 1)
It's given that T(n) = (-1)ⁿ n²
So S(2n +1) - S(2n - 1)
= T(2n) + T(2n + 1)
= (-1)²ⁿ x (2n)² + (-1)^(2n+1) x (2n +1)²
= ((-1)²)ⁿ x (4n²) + (-1)¹ x ((-1)²)ⁿ x (4n² + 4n + 1)
= 1ⁿ x 4n² - 1 x 1ⁿ x (4n² + 4n + 1)
= 4n² - 4n² - 4n - 1 (realise that 1ⁿ just = 1)
= - 4n - 1 (proved)
Thanks bro. Understood.
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done
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clear
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Pls help me .Appreciate your help
Date Posted:
6 years ago
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