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Railways Sample Paper RRBs Assistant Loco Pilot and Technician CBT STAGE-I Sample Paper-32

  • question_answer
    Given that\[1+2+3...+\frac{x(x+1)}{2},\] then 1+ 3 +5 +?.+ 99 is equal to

    A)  2250   

    B)  2500

    C)  2525               

    D)  3775

    Correct Answer: B

    Solution :

    \[1+2+3+...+x=\frac{(x+1)}{2}\] \[\therefore \]\[1+3+5...+99\] \[=(1+2+3+4+5+...+100)-(2+4+6+...100)\]     \[=\frac{100(100+1)}{2}-21\,(1+2+3+...50)\] \[=\frac{100\times 101}{2}-\frac{2\times 50\times 51}{2}\] \[=50\times 101-50\times 51\] \[=50(101-51)\] \[=50\times 50=2500\]


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