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CBSE Class 10 Answered

Please solve this question 
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Asked by vikasg13.hardware | 30 Jun, 2018, 07:02: AM
answered-by-expert Expert Answer
begin mathsize 16px style Rationalize
fraction numerator 1 over denominator square root of straight k plus 1 end root plus square root of straight k end fraction
equals fraction numerator square root of straight k plus 1 end root minus square root of straight k over denominator open parentheses square root of straight k plus 1 end root plus square root of straight k close parentheses open parentheses square root of straight k plus 1 end root minus square root of straight k close parentheses end fraction
equals square root of straight k plus 1 end root minus square root of straight k
straight S subscript straight n equals sum from straight k equals 0 to straight n of open parentheses square root of straight k plus 1 end root minus square root of straight k close parentheses equals square root of 1 minus 0 plus square root of 2 minus square root of 1 plus square root of 3 minus square root of 2 plus...... plus square root of straight n plus 1 end root plus square root of straight n
straight S subscript straight n equals square root of straight n plus 1 end root
straight S subscript straight n minus 1 end subscript equals square root of straight n
So
fraction numerator 1 over denominator square root of straight n plus 1 end root plus square root of straight n end fraction
rationalise
square root of straight n plus 1 end root minus square root of straight n
straight S subscript straight n equals sum from straight n equals 0 to 99 of open parentheses square root of straight n plus 1 end root minus square root of straight n close parentheses equals square root of 99 plus 1 end root equals 10
end style
Answered by Arun | 14 Jul, 2018, 05:50: PM
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