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Question 5 : Let a_{1} , a_{2} be integers such that a_{1} - a_{2} + a_{3} - a_{4} + ........ +(-1)^{n-1} a_{n} = n , for n ≥ 1. Then a_{51} + a_{52} + ........ + a_{1023} equals

- -1
- 1
- 0
- 10

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Given that a_{1} - a_{2} + a_{3 }- a_{4} + ........ +(-1)^{ n-1} a_{n} = n

So, a_{1} = 1

a_{1} - a_{2} = 2 => a_{2} = 1-2 = -1

a_{1} - a_{2} + a_{3} = 3 => a_{3} = 1

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

Then a_{51} + a_{52} + ........ + a_{1023 }= 1 + (-1) + .... + 1

a_{51} + a_{52} + ........ + a_{1023 }= 1

The question is **"Let a _{1} , a_{2} be integers such that a_{1} - a_{2} + a_{3} - a_{4} + ........ +(-1)^{n-1} a_{n} = n , for n ≥ 1. Then a_{51} + a_{52} + ........ + a_{1023} equals" **

**Choice B** is the correct answer.

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