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If the Mth term of an …

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If the Mth term of an AP be 1/N and its Nth term be 1/M then show that its (MN)th term is 1.

    • Posted by Uzzwal Upadhyay 7 years ago

    CBSE > Class 10 > Mathematics
    • 2 answers

    Uzzwal Upadhyay 7 years ago

    tnx bhai....

    1Thank You

    Gaurav Seth 7 years ago

    Given that, mth term=1/n and nth term=1/m.
    then ,let a and d be the first term and the common difference of the A.P.
    so a+(m-1)d=1/n...........(1) and a+(n-1)d=1/m...........(2).
    subtracting equation (1) by (2) we get,
    md-d-nd+d=1/n-1/m
    =>d(m-n)=m-n/mn
    =>d=1/mn. 
    again if we put this value in equation (1) or (2) we get, a=1/mn.
    then, let A be the mnth term of the AP
    a+(mn-1)d=1/mn+1+(-1/mn)=1 
    hence proved.

    2Thank You

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