1.

If mth term and nth term of an ap be 1/n and 1/m then show tha its (mn)th term is 1

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Answer:

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.

Step-by-step explanation:


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