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JEE Advanced Mathematics question

MathematicsSequence and SeriesJEE Advanced

The sum of to is

Answer: (B)

Solution

The series is

S=Missing argument for \frac\frac2{10}+Missing argument for \frac\frac4{}+Missing argument for \frac\frac6{}+Missing argument for \frac\frac8{}+,

an arithmetico-geometric series (numerators in AP, denominators in GP with ratio ). Multiply by and subtract:

S-

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Question ID VK-107839