Miraculous tree

Miraculous tree grows so fast that the first day increases its height by half the total height of the second day by the third, the third day by a quarter, etc. How many times will increase its height after 6 days?

Correct result:

n =  4

Solution:

$n=1 \cdot \ (1+1/2) \cdot \ (1+1/3) \cdot \ (1+1/4) \cdot \ (1+1/5) \cdot \ (1+1/6) \cdot \ (1+1/7)=4$

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