sábado, 4 de febrero de 2017

1295. How many fractions must be added?

    Dear Teacher:
    If  there were  n  fractions and we rationalized all of them then

− √1 + √2 − √2 + √3 − √3 + √4 − √4 + √5 − √5 + √6 ...  =  − 1 + √(n+1)  =  1000
√(n+1)  =  1000 + 1  =  1001
n + 1  =  10012  =  1002001
n  =  1002001 − 1  =  1002000  =  One million two thousand fractions.

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