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SSC Sample Paper SSC CGL - Sample Paper-14

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

    A) 2250                

    B) 2500

    C) 2525                            

    D) 3775

    Correct Answer: B

    Solution :

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


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