class 11
sequence and series
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Answer:Given,
(a/1-a) + (b/1-b) + (c/1-c) = 1
Add 1 to 1st term on LHS, add 1 to second term and again 1 to last term. Balance this by adding 3 to the RHS.
[(a/1-a) + 1 ] + [(b/1-b) + 1 ] + [ (c/1-c) + 1] = 1 + 3
Perform the operations within the three square brackets on LHS and get,
(a + 1 - a)/(1-a) + (b+1-b)/(1-b) + (c + 1-c)/ (1-c) = 4
Simplifying the quantities within round brackets on LHS, we obtain
(1/1-a) + (1/1-b) + (1/1-c) = 4 (Q.E.D.)
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