InterviewSolution
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InterviewSolution
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If Mth term of an A.P. is 1÷n and the nth term is 1÷m then find the sum of its first mn term |
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Answer» Let a and d be the first term and common difference respectively of the given AP,then\xa0mth\xa0term = a+(m-1)d ==> a+(m-1)d = 1/n -----(1)\xa0and nth\xa0term=a+(n-1)d ==> a+(n-1)d = 1/m -----(2)\xa0subtracting (2) from (1), we have Let the first term of the A.P be \'a \' and its common difference be \'d \'Now, mth term of the A.P is 1/nwhich means, a + (m - 1)d = 1/n --- (i)Again,its nth term is 1/mwhich means, a + (n - 1)d = 1/m --- (ii)on substracting eqn. (ii) from (i) we get,a + (m - 1)d - a - (n - 1)d = 1/n - 1/m=> d (m - 1 - n + 1) = (m - n)/mn=> d (m - n) = (m - n) / mn=> d = 1/mnso, a = 1/m - (n - 1)(1/mn) = n - n + 1 / mn =1/mnie., a = d = 1/mnNow, Smn = mn/2 [2a + (mn - 1)d]= mn/2 [2/mn + (mn - 1)1/mn]= mn/2 [2 + mn - 1]/mn= (mn + 1)/2 mn+1by2 |
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