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    Question

    src="https://www.ixambee.com/questionimage/Chapter/1647411908-s6.png" alt="" />
    A 6179/15275 Correct Answer Incorrect Answer
    B 6070/14973 Correct Answer Incorrect Answer
    C 7191/15174 Correct Answer Incorrect Answer
    D 5183/16423 Correct Answer Incorrect Answer

    Solution

    This series consists of two different series one having 2 numbers as product in denominator and the other has three numbers as product in the denominator lat terms in each series is  1 / 19×21×23 and 1 /28×31 1 / 1×3×5 + 1 / 1×4 + 1 / 3×5×7 +  1 / 4×7 +  1 / 5×7×9 +  1 /7×10 +……. upto 20 terms = 1 / 1×3×5 + 1 / 3×5×7 + 1 / .. 1×4 + 1 / 4×7 + . . = 1 /4 (1 / 1×3 −  1 / 3×5 + 1 / 5×7 + 1 / 7×9 ... – 1 / 21×23 + 1 / 1×3 ( 1 / 1− 1 / 4 + 1 / 4 – 1 / 7 .. – 1 / 31) = 1 /4(1 /  1×3 – 1 / 21×23 ) + 1 / 1×3 (1 / 1 – 1 / 31) = 40 / 483 + 10 / 31 = 6070 / 14973

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