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Question 85
There are 8436 steel balls, each with a radius of 1 centimeter, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth, and so on. The number of horizontal layers in the pile is
Solution
For the given problem ,
$$\sum {n(n+1)/2} = 8436 $$ which is
$$\sum {n^2/2} + \sum{n/2} = 8436 $$ which is equal to
n*(n+1)(2n+1)/12 + n*(n+1)/4 = 8436 , solving we get n=36.
Solving the equation might be lengthy. you can substitute the values in the options to arrive at the answer.
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