Result number of filled briquettes

There's a bunch of coal balls , Pile up in a triangular pyramid . Specifically ：
On the first floor 1 individual ,
The second floor 3 individual （ In a triangle ）,
The third level 6 individual （ In a triangle ）,
The fourth level 10 individual （ In a triangle ）,
....
If there is 100 layer , How many coal balls are there ？

Please fill in the number of coal balls .

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answer

171700

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The problem solving process

The clear topic is 1~100 The sum of coal briquettes , Then this topic must have rules . Here, the law of the number of briquettes in each layer is analyzed ：

first floor ：1

The second floor ：1+2

The third level ：1+2+3

The fourth level ：1+2+3+4

……

The hundredth floor ：1+2+……+100

Obviously, the number of each layer is an arithmetic sequence , The arithmetic sequence formula ：Sn=(a1+an)*n/2

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Attach code

#include<iostream>
using namespace std;
int main()
{
	int sum=0;
	int n;
	cin>>n;
	for(int i=1;i<=n;i++)
		sum+=(1+i)*i/2;
	cout<<sum<<endl;
	return 0;
}