### PROBLEM LINK:

**Author:** Nishchith Shetty

**Tester:** Karan Sheth

**Editorialist:** Chirag Shetty

### DIFFICULTY:

Easy

### PREREQUISITES:

Simple Math

### PROBLEM:

Given an integer **n** you have to print result adding all even nos till n and subtracting all odd nos tll n.

### EXPLANATION:

Since n is very large adding even nos one by one and subtracting odd nos one by one will give you TLE.

There are 2 simple cases.

- If
**n**is even (say 10) then answer is n/2 (i.e 5)

If n is even then we can consider first n/2 odd numbers and

and first n/2 even numbers excluding 0 as 0 won’t add up to the sum.

For eg if n=10,

Odd nos - 1 3 5 7 9

Even nos - 2 4 6 8 10 (excluding 0)

Let k = n/2 (i.e 5)

Using sum of Arithmetic Progression Formula :

S = (k/2)*(2a+(k-1)*d)

Sum of even numbers (a=2,d=2)

S1 = (k/2)*(4+(k-1) 2)
S1 = (k/2)(2k+2)
S1 = k*k+k

Sum of odd numbers (a=1,d=2)

S2 = (k/2)*(2+(k-1) 2)
S2 = (k/2)(2k)
S2 = k*k

S1-S2 = k = n/2

- If
**n**is odd (say 9) then answer is -(n+1)/2 (i.e -5)

If we take n+1 then that is even and we just need to subtract the last even number i.e n+1 from above formula.

i.e (n+1)/2-(n+1) = -(n+1)/2

### ALTERNATIVE SOLUTION

Observations skills

### AUTHOR’S AND TESTER’S SOLUTIONS:

Author’s solution can be found here.

Tester’s solution can be found here.