Building Tower

★★★★★

1 votes

, Basic Math, C++, Math, Observation

Details

Problem

Alex wants to build a tower of height $N$ levels. He wants to build the tower as follows: the $i^{th}$ level of the tower must have $1 + 2 + ... + (i - 1) + i$ blocks, i.e., the top level of the tower must consist of $1$ block, the second level must consist of $1 + 2 = 3$ blocks, the third level must have $1 + 2 + 3 = 6$ blocks, and so on. The numbering of levels is done from top to bottom.

Find the total number of blocks required to build a tower of height $N$ .

Input Format:

The first line contains an integer $T$ , which denotes the number of test cases.
The first line of each test case contains one integer $N$ , denoting the height of the tower.

Output Format:

For each test case, print the total number of blocks required to build a tower of height $N$ .

Constraints:

$1 <= T <= 10^3$

$1 <= N <= 10^5$

Time Limit: 2

Memory Limit: 256

Source Limit:

Explanation

For first test case:
$N=4$ , Alex uses $1$ block on the $1^{st}$ level, $3$ blocks on the $2^{nd}$ level, $6$ blocks on the $3^{rd}$ level, and $10$ blocks on the $4^{th}$ level of the tower. So, the total number of blocks required is $1 + 3 + 6 + 10= 20$ . Hence, $20$ is the answer.

For second test case:
$N=1$ , Alex uses $1$ block on the $1^{st}$ level of the tower. So, the total number of blocks required is $1$ . Hence, $1$ is the answer.