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Asked by vikasg13.hardware | 30 Jun, 2018, 07:02: AM
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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, 17:50: PM

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