Look for patterns and state a general conjecture regarding the sums for
+1 +2 +3 ‡4 ‡5….. +6
In
where n is any whole number greater than 1.
Upon observing the given sum, it can be noticed that the sequence alternates between positive and negative numbers. Additionally, the sum increases by 1 with each subsequent term until it reaches 4, and then decreases by 1 with each subsequent term until it reaches -5.
Based on this pattern, a conjecture can be made that the sum of the sequence +1 +2 +3 ‡4 ‡5….. +6 for any whole number n greater than 1 can be expressed as:
sum = (-1)^(n+1) * ((n+4) * (n-1))/2