Question

the sum of all even integers between 1 and 100 is 2550 ,then sum of all odd integers between 50 &150 ???

Answer 1

The sum of the first n odd numbers is n^2, where n is the number of terms.

In this case, we can find the sum of all odd integers between 50 and 150 can be calculated as the difference between the first n odd integers up to 150 and 50.

An odd integer is given by the term, 2n-1.

So, when 2n-1 = 49, we can find the value of n.

2n = 49 + 1 = 50. Thus, n = 50/2 = 25.

Therefore, the sum of 25 odd numbers, till 49 = 25^2.

Similarly, equating 2n - 1 = 149, we get the value of n = (149+1)/2 = 150/2 = 75.

So, the sum of first 75 odd numbers, till 149 = 75^2.

Thus, the sum of odd numbers between 50 and 150 is the difference of 75^2 and 25^2.

75^2 - 25^2 = (75+25) * (75-25)
                    = 100 * 50
                    = 5000.

Thus, the sum of the odd numbers between 50 and 150 is 5000.