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CBSE Class 9 Answered

1/1+√2+1/√2+√3+1/√3+√4+1/√4+√5+1/√5+√6+1/√6+√7+1/√7+√8+1/√8+√9=2
Asked by Dhirajkumar0812005 | 25 May, 2019, 07:23: AM
answered-by-expert Expert Answer
begin mathsize 16px style straight L. straight H. straight S space equals fraction numerator 1 over denominator 1 space plus space square root of 2 end fraction plus space fraction numerator 1 over denominator square root of 2 begin display style space end style begin display style plus end style begin display style space end style begin display style square root of 3 end style end fraction space plus space..... space plus space fraction numerator begin display style 1 end style over denominator begin display style square root of 8 space plus space square root of 9 end style end fraction space space space
fraction numerator begin display style 1 end style over denominator begin display style 1 space plus space square root of 2 end style end fraction cross times fraction numerator 1 space minus space square root of 2 over denominator 1 space minus space square root of 2 space end fraction equals space fraction numerator 1 space minus space square root of 2 over denominator 1 squared minus space open parentheses square root of 2 close parentheses squared end fraction equals space fraction numerator begin display style 1 space minus space square root of 2 end style over denominator begin display style 1 minus space 2 end style end fraction equals space square root of 2 space minus space 1
Similary space rationalise space all space the space term comma space we space get
straight L. straight H. straight S space equals space minus 1 plus space square root of 9 equals space minus 1 space plus space 3 space equals space 2 equals straight R. straight H. straight S
Hence space proved.
end style
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