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JEE Advanced Mathematics question

MathematicsSequence and SeriesJEE Advanced

Let be points on the number line such that are in GP where is the origin, and the common ratio of the GP be a positive proper fraction. Let be the middle point of the line segment . Then the value of is equal to

Answer: (B)

Solution

Let be the common ratio, so ; with a positive ratio all lie on the same side of . The midpoint of is at distance

==(1+.

Summing the geometric series ():

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Question ID VK-109922