What is 1 plus 2 plus 3 plus ..to 100?

Answer 1

1+2+3.......+100 forms an ending arithmetic progression. There are two ways this can solved as follows-

1) the old an boring way of adding them up and getting an answer of 5050.

2)This step will involve the knowledge of Arithmetic Progressions. An AP is such a sequence of the numbers that each number will have common difference between it and its predecessor.

There is a certain formula given for solving the sum of the terms of an AP, which is

S=n(T+a)/2 where n is the number of terms of he AP, T is the final term and a is the first term. Putting the values-

S=100(100+1)/2= 50(101)= 5050.

Practically this method can be explained in this fashion- If you add one with 100, you get 101. Similarly 99+2= 101, 98+3=101.......till 50+51=100. We get 50 such pairs, therefore the sum os 50 into 101=5050

1+2+3...50+51......+98+99+100=(1+100)+(2+99)+(3+98)........+(50+51)=

(101)+(101)......50 times, therefore 1+.......100=50(101)=5050