What is th remainder when the sum of the first 102 counting numbers is divided by 5220?
You can find the sum of the first 102 counting numbers using Gauss's method, namely:
"the sum of the first n counting numbers is n*(n+1)/2" whether n is odd or even.
For n = 102, the sum is 102*103/2=10506.
So divide 10506 by 5220 to get a quotient of 2, with a remainder of 66.
Mental calculation tip:
To multiply two numbers close to a hundred can be done in the head as follows, no paper, no calculators:
Let the numbers be (100+x) and (100+y), where x and y are small numbers. Take the example of 102 and 103, then x=2, y=3.
Start with the left most digit, which is a 1.
The next two digits are the sum of x and y, that gives 105.
The next two digits are the product of x and y, that gives 10506, et voilà!
Try with 107*109, that should give 11663.
Forgot to divide 10506 by 2 according to Gauss's rule:
10506/2=5253, divided by 5220 gives a quotient of 1 with 33 as a remainder, and divided by 5250 gives a quotient of 1 and 3 as a remainder.
i have no clue i am tring ti find the answer
To find the remainder when the sum of the first 102 counting numbers is divided by 5220, we need to calculate the sum of these numbers and then perform the division.
The sum of the first n counting numbers can be found using the formula: S = (n/2) * (first number + last number), where S is the sum, n is the total number of terms, and the first number and last number are the first and last terms in the sequence.
In this case, we want to find the sum of the first 102 counting numbers, so n = 102 and the first number is 1, while the last number is 102.
Using the formula, the sum of the first 102 counting numbers is:
S = (102/2) * (1 + 102)
= 51 * 103
= 5253
Now, to find the remainder when this sum is divided by 5220, we perform the division:
Remainder = 5253 % 5220
To calculate this, we divide 5253 by 5220 and find the remainder. The remainder operator (%) gives us the remainder left after the division. In this case:
Remainder = 5253 - (5253 / 5220) * 5220
= 5253 - (1 * 5220)
= 5253 - 5220
= 33
Therefore, the remainder when the sum of the first 102 counting numbers is divided by 5220 is 33.