0
The total T of adding numbers from 1 to n is (n x (n+1))/2; consider if n=10:
adding 1+ 2+ 3+...+ 8+ 9+ 10= T and
adding 10+ 9+ 8+...+ 3+ 2+ 1= T (the same answer)
Now add the the two lines together--->
11+11+11+..+11+11+11= 2T, so there are 10 11s
10 x 11 =2T, divide both sides of the equal sign by 2
(10 x 11)/2 =T
So, where n=10, T=55
Still curious? Ask our experts.
Chat with our AI personalities
Fran
Maxine
JordanAdd your answer:
Earn +20 pts
What are all the numbers from 1 to 99 added up to?
Consider that 1+99=100 and 2+98=100 you can continue all the way to 49+51=100. This means you have (49x100)+50 (as fifty was left at the end) this gives a final answer of 4950
If you added all the numbers between 1 and 100 including 1 and 100 how much is it?
Taking all the extreme numbers between 1 and 100 in each sum gives 1 + 100, 2 + 99, 3 + 98... and so on - fifty pairs of sums which add to 101. Therefore, the sum of the integers between 1 and 100 is equal to 50 x 101 = 5050.
What is he average of 96 100 and 92?
To find the average of a set of numbers, you add all the numbers together and then divide by the total number of values. In this case, the sum of 96, 100, and 92 is 288. Dividing 288 by 3 (the total number of values) gives an average of 96.
What is the sum from all the odd numbers from 1 to 100?
The sum of all the odd numbers from 1 through 100 is 10,000
What is the sum of all the first 100 even numbers?
The sum of all the first 100 even numbers is 10,100.
