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Sum Of Squares Of First N Natural Numbers

Easy

0/40

Average time to solve is 15m

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7 upvotes

Asked in companies

Problem statement

You are given an integer 'N'. You need to find the sum of squares of the first 'N' natural numbers.

For example:

If 'N' = 4. You need to return 1^2 + 2^2 + 3^2 + 4^2 = 30.

Detailed explanation ( Input/output format, Notes, Images )

Input Format:

The first line of input contains a single integer 'T', representing the number of test cases or queries to be run. 
The first and the only line of each test case contains an integer 'N'.

Output Format:

For each test case, return the sum of squares of the first 'N' natural numbers in a single line.

Constraints:

1 ≤ T ≤ 10^4
1 ≤ N ≤ 5*10^5

where 'T' is the number of test cases and 'N' is the given number.
Time Limit: 1 sec.

Note:

You are not required to print the expected output, it has already been taken care of. Just implement the function.

Sample Input 1:

Sample Output 1:

30
1
91

Explanation of Input 1:

The first test case has already been explained in the problem statement.
For the second test case, 'N' = 1. So the sum would be =  1^2 = 1.
For the third test case, 'N' = 6. So the sum would be =  1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 = 91.

Sample Input 2:

Sample Output 2

650
6
285

Hint 1

Hint 2

Hint 3

Sum the squares of first ‘N’ natural numbers.

Approaches (3)

Approach 1

Approach 2

Approach 3

Brute Force - Recursive

Write a recursive solution for adding the sum of the squares of the first ‘N’ natural numbers.
The base case would be the sum of the first natural number, which is 1.
Sum up the squares of each number from 1 to ‘N’.
Finally, return this sum.

Time Complexity

O(N), where ‘N’ is the given number.

Since we are traversing from 1 to ‘N’.

Space Complexity

O(N), where ‘N’ is the given number.

Considering the recursive stack space.

(100% EXP penalty)

Sum Of Squares Of First N Natural Numbers

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