1 3 5 49 simple algorithm?

Solution: sum = 1 + 3 + 5 + ...+47+49, then sum =49+47+....+5+3+1, and +sum = (1+49)+(3+47)+(5+45)+....45+5)+(47+3)+(49+1)=50+50+50…+50+50=50 25=750, sum+and=750, and 2=750, sum=375

1 to 49 is 49 numbers, remove the middle number 25 and there are 48 numbers left, and the sum of the first and last two numbers of the remaining 48 numbers is 50, that is, there are 12 50s, and then add 25 to be the sum. ）

The simple algorithm is to change their position! The sum of 1 and 49 is equal to 50, and the sum of 3 and 47 is equal to 50, so there are 12 50s in total, and finally there is a 15 left in the middle, which adds up to 12 50 + 25 = 625

1+3+5+..The simple algorithm for 49 is calculated using Gauss's theorem, which is as follows:

In fact, it is 1+3+5+...49=(1+49)+(3+47)+(5+45)+.25=625

1+3+5+…The simple algorithm of +49 is the commutative and associative properties of addition.

According to the question, it can be concluded that it is the sum of singular numbers within 1 50. First of all, we can see that 1+49=50, and 3+47 is also equal to 50

In this way, you can find out the pattern. The sum of the two numbers is equal to 50, then first calculate how many odd numbers there are in 1 49, there are 25, then 25 2 = that is, 50 12 + 25 = 625

Solution: Original formula = (1+49) [49-1) (3-1)+1] 1 2

The 6th grade method will do, thank you!

+48=50, and so on, add to 24+26 for a total of 24 groups, leaving a 25 original = (1+49)+(2+48)+.24 + 26) + 2550x (48 divided by 2) + 25

50x24+25

There are a total of 25 odd numbers in this set of numbers, so the original formula = (1+49)+(3+47)+(5+45)+....25

25x25

The sum of the difference series = the middle number x the number.

1, 3, 5 up to 49 is a total of 25 numbers, 1 + 49 = 50, 3 + 47 = 50, a total of 12 pairs of such numbers add up to 50, and there is a middle number 25, 50 times 12 + 25 = 625

The number of flames is equal to a few times a few times a few times a few.

Original: 1+2+3+4+5+6.....99

1 1099) 10 (2 1098) ....Ten (49 dec. 51) ten 50100 49 dec. 50

100x49 ten 50

4900 out of 10

Please refer to it!

1 1099) 10 (2 1098) ....Ten (49 dec. 51) ten 50100 49 dec. 50

100x49 ten 50

4900 out of 10

Solution: Law 1 99...2+98……48+52..49 + 51 are equal to 100, that is, 99 numbers, one 50, one number, more than 98 2 (1 9) 49 100

1＋99）x49＋50

You can put 1+2+3+....+99 is seen as 50 100s, and 1+2+3+....There is only one 50 in +99, so the final result is to subtract 50, so we get:

Original 5ox99 4950

1+2+3 +98+99 is the difference series. The sum of its first n terms is the product of the middle value (50) and the total number of terms (99).

The sum of the first and last is 100, and there are 99 2 such numbers. So 100 99 2 = 4950.

1 1099) 10 (2 1098) ....Ten (49 dec. 51) ten 50100 49 dec. 50

100x49 ten 50

4900 out of 10

Or use n(n+1)2

Get 99(99+1) 2=4950

Let's take the equation 1+2+3+4+5+6 ......... first99 is written as (1+99)+(2+98)+(3+97)+(4+96)+(5+95)+(6+94)....+50

Then the equation = 100 49 + 50

The final equation = 4900 + 50 = 4950

This is the sum of the series of equal differences.

First + Last) Number of Terms: 2

Add one head and one tail in turn, a single 50, as follows:

The answer is to add the first and last digits multiplied by 49 plus 50, and generally half of the numbers are multiplied by the sum of the first and last digits plus the middle number.

Find the sum of the roll:

First + Last) Number of Terms: 2

First term (first number) = 1

Last letter file item (last digit big open finger) = 100

Number of items (how many numbers) = 100

So (1+100)*100 2=5050

Analysis: 1 to 100 a total of 100 numbers, the beginning and end of each add, such as 1 + 100, 2 + 99, all the way to 50 + 51, divided into 50 items, the value of each Fan Dan is 101, then 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + ...100=101*50=5050。

1+100）dao+（2+99）+（3+98）+.50+51) Extended Data: A Simple Calculation Method:

1. "Rounding up and ingenious calculation" - the commutative law of addition and the combination law of state disturbance.

Make the calculations. 2. Use the commutative law and associative law of multiplication to perform simple calculations.

3. Use the properties of subtraction macro or for simple calculation, and pay attention to the reverse progress.

4. Use the nature of division to make a simple calculation (divide by a number, first multiply the reciprocal of a number, and then distribute).

5. Use the multiplicative distributive law.

Make a simple calculation. 6. Mixed operation (according to the law of mixed operation).

There is no one rule for your equation, how can you determine the next one?

If you keep subtracting after that, it will end up being a negative number.

1+2-3+4+5-6-……Pai Xinliang -99 = 1-1 + 9 - (6 + 7 + 8 + 9 + ......99)=9-105×94÷2=9-105×47=9-4935=-4926。You refer to the slow answer of the dust kuan!

Answer: According to the meaning of the question, it can be concluded that the original deformation is, 1+3+5+....+45+47+49=(1+49)+(3+47)+(5+45)+…25x50=1250。

Hello dear The answer is as follows: 1+3+5+7+9......+45+47+49＝(1+49)×25÷2=50×25÷2=1250÷2=625

Problem solving idea: 1 50 has a total of 50 natural numbers, so there are odd numbers 50 = 2 = 25 1 + 49 = 50, 3 + 47 = 50 Therefore, for every two numbers in a group, their sum is 50 so that 252 groups can be formed, so: 1 + 3 + 5 + 7 ......+45+47+49=50×25÷2=625

Extended Information: 1. Addition Commutative Law: 1. Definitions:

The commutative law of addition is one of the laws of mathematical calculation. Refers to the addition of two additions, the exchange of the position of the additions, and the unchanged. 2. Examples:

The law of commutative addition: 20 + 480 = 480 + 203, the law of commutative law of addition Limitations: Although this law seems to be obvious to everything, it is not.

In the absence of time in space (within three dimensions), the additive commutative law is perfectly correct. But once there is a timeline, this law does not hold.

Using the first n terms of the equal difference series and the formula, s = (first term + last term) number of terms 2=(1+49) 25 2=625.

1+3+5+……Simple arithmetic of 45+47+49? Using the first n terms of the equal difference series and the formula, s = (first term + last term) number of terms 2=(1+49) 25 2=625.

1+3+5+7+……199 easy to calculate.

Analysis: This problem can be solved directly by using the knowledge of number sequences, which is relatively simple; It is also possible to divide a total of 100 numbers into 50 groups with a group of closing numbers, such as 1 and 195 ......99 and 101, the sum of each group is 200, multiplied by the number of groups is the result. Answer:

This is the calculation.

Use the knowledge of the sequence to solve:

This is also the result.

So, 1+3+5+7+......199 The result of a simple calculation is 10000.

Okay, this question is finished, if you still don't understand, welcome to continue to ask me in the follow-up question.

Add the beginning and the end to make up the whole number.

From 1 to 200, there are 100 odd and even numbers, that is, from 1 to 199 there are 100 odd numbers, and the combination of the beginning and the end can form 50 pairs, and the sum of each pair is 200, that is.

1 + 199) Ten (3 Ten 197) Ten (5 Ten 195) Ten (......Ten (99 ten, 101) = 200x5o = 10000

Calculated with an equal difference formula. After you dive into the story, you will find that this problem is very, very simple, and can also be calculated using Newton's algorithm of adding one to 100.

200 (1 to 99 to see how many odd numbers there are).

This question is the addition of odd terms, in fact, it is relatively easy to add by combining the front and back terms:

This problem is much easier to calculate in this way.

1+49+3+47+5+45+…+23+27+25 is the sum of the end. If you want the formula for this series, you can ask again.