Much easier this way:

1 2 3 .... 98 99 100
100 99 98 .... 3 2 1

Add the top number below it they all add to 101.

100+1=101
99+2=101
98+3=101

There are 100 101's, therefore 100x101= 10100. 10100 is total of two sets of 100's, we need total sum of one set. So we 10100/2=5050. Simple rule is add one to the Last digit i.e. 100 and make it 101 time it by the origial number, devide by 2. So the TRUTH/RULE is:

n +1 x n / 2 = total sum of n

Suppose we want to find out total sum of 785 therefore n is 785.

785+1x785/2 =308505

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