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Question 5 : Let a1 , a2 be integers such that a1 - a2 + a3 - a4 + ........ +(-1)n-1 an = n , for n ≥ 1. Then a51 + a52 + ........ + a1023 equals
Given that a1 - a2 + a3 - a4 + ........ +(-1) n-1 an = n
So, a1 = 1
a1 - a2 = 2 => a2 = 1-2 = -1
a1 - a2 + a3 = 3 => a3 = 1
So, the series proceeds as 1, -1, 1, -1, ...
Then a51 + a52 + ........ + a1023 = 1 + (-1) + .... + 1
a51 + a52 + ........ + a1023 = 1
The question is "Let a1 , a2 be integers such that a1 - a2 + a3 - a4 + ........ +(-1)n-1 an = n , for n ≥ 1. Then a51 + a52 + ........ + a1023 equals"
Choice B is the correct answer.
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