Discussion

Explanation:

Given that a₁ - a₂ + a₃ - a₄ + ........ + (-1)^n-1 a_n = n

Put n = 1 ⇒ a₁ = 1

Put n = 2 ⇒ a₁ - a₂ = 2 ⇒ a₂ = 1 - 2 = -1

Put n = 3 ⇒ a₁ - a₂ + a₃ = 3 ⇒ a₃ = 3 – 1 -1 = 1

Hence, the series proceeds as 1, -1, 1, -1, ...

i.e. odd term of the series = +1

& even terms of the series = -1

Then a₅₁ + a₅₂ + ........ + a₁₀₂₃ = 1 + (-1) + .... + 1

⇒ a₅₁ + a₅₂ + ........ + a₁₀₂₃ = 1

Hence, option (b).

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