Question 6 - Figure it out - Page 143, 144 - Chapter 6 Class 7 - Number Play - Ganita Prakash

Transcript

Question 6 (Method 1) What is the parity of the sum of the numbers from 1 to 100? In the numbers from 1 to 100, there are 50 odd numbers and 50 even numbers. The sum of the 50 odd numbers is even (an even number of odds). The sum of the 50 even numbers is even. The total sum is Even + Even = Even Thus, sum of numbers from 1 to 100 is even We can also do with another method Question 6 (Method 2) What is the parity of the sum of the numbers from 1 to 100? Let’s add all the numbers from 1 to 100: 1 + 2 + 3 + … + 99 + 100 Let’s make pairs: (1 + 100), (2 + 99), (3 + 98), … Each pair adds up to 101. Now, how many pairs are there? There are 100 numbers total, so 50 pairs. Each pair = 101 So the total = 50 × 101 = 5050 Since 5050 ends with a 0, and any number ending in 0 is even. So, the sum of numbers from 1 to 100 is even.