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Find the sum of n terms of the series 1/(√1+√3)+ 1/(√3+√5)+1/(√5+√7)+........upto n terms
Answer is nChange every term in difference of 2 terms by multiplying and dividing by 2After this- 2 in numeratorcan be written as=3-1=5-3=7-5....=2n+1-2n-1 then rationalise every term . You will fond that starting term get cancelled by ending term of succedding groupof term=1/2(2n+1-1)=n Here i cannot write the answer as i do not know how to write squre root
N th term is 1 / √2n-1+√2n+1.On rationalizing we get√2n+1-√2n+-1 / 2We can write it as √2n+1/ 2 - √2n-1 / 2Star puting values in the above eq. Tema will start canceling out and we get √2n+1 / 2 - 1/2 = 1/2 {(√2n+1)-1}
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