JEE Main & Advanced Mathematics Sequence & Series Question Bank Arithmetic Progression

  • question_answer
    The ratio of the sums of first \[n\] even numbers and \[n\] odd numbers will be

    A) \[1:n\]

    B) \[(n+1):1\]

    C) \[(n+1):n\]

    D) \[(n-1):1\]

    Correct Answer: C

    Solution :

    Let \[{{S}_{Even}}=2+4+6+8+........\infty \]         ?..(i) and \[{{S}_{Odd}}=1+3+5+7+9+.......\infty \]    ?..(ii) Sum \[c\] and \[{{S}_{O}}=\frac{n}{2}[2+(n-1)2]=\frac{n}{2}(2n)\] Now  \[\frac{{{S}_{E}}}{{{S}_{O}}}=\frac{(n+1)}{n}\] or \[{{S}_{E}}:{{S}_{O}}=(n+1):n\].


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