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The formula 1 + 2 + 3 + 4 +. + 100 represents the sum of 100 natural numbers starting from 1. Because the formula is relatively long, the writing is not square For the sake of simplicity, we will express it as ∑ (100 above, n = 1 below, N in the middle). Here is the summation sign. Through reading the above materials, we can calculate ∑ (2014 above, n = 1 below, 1 / N of n (n + 1) at the opening in the middle)
The final result is 1-1 / (n + 1)!
Observe the following equations: 3 ^ 1 = 3, 3 ^ 2 = 9, 3 ^ 3 = 27, 3 ^ 4 = 81, 3 ^ 5 = 243, 3 ^ 6 = 729, 3 ^ 7 = 2187 You can find 3 ^ n (n is an unnatural number)
Do you know the law of the last number? Write the last number of 3 ^ 2013 according to the law you found
3^1=3,
3^2=9,
3^3=27,
3^4=81,
3^5=243,
3^6=729,
3^7=2187
...
The last position is 3,9,7,1
2013 △ 4 = more than 503 1
The last digit of 3 ^ 2013 is 3
For any natural number n, when n is odd, add 121, when n is even, divide by 2, this is an operation. Now, if you operate on three digit 241 continuously, will 100 appear in the operation process, why?
241+121=362，362÷2=181；181+121=302，302÷2=151；151+121=272，272÷2=136，136÷2=68，68÷2=34，34÷2=17；17+121=138，138÷2=69；69+121=190，190÷2=95；95+121=216，216÷2=108，108÷2=54，54÷2=27；27+...
RELATED INFORMATIONS
- 1. Let n be a natural number, and use the algebraic expression containing n to express: 1. Three consecutive integers; 2. Two adjacent even numbers; 3. Two adjacent odd numbers
- 2. In natural numbers, the smallest even number is (), and the smallest odd number is ()
- 3. There are five consecutive odd numbers whose product is 328 185. Find these five natural numbers
- 4. There are four natural numbers which are not equal to each other. The difference between the maximum number and the minimum number is equal to 4. The product of the minimum number and the maximum number is an odd number, and the sum of these four numbers is the smallest two odd numbers. What is the product of these four numbers?
- 5. Is the proposition "the sum of the product of four continuous positive integers and 1 must be a complete square number"
- 6. A four digit number can be divided by two consecutive two digit numbers. If the four digit number is divided by one of them, the quotient is 141. If the four digit number is divided by the other, the quotient is larger than 141. The four digit number is 141
- 7. Divide four digits by two digits and divide 50 channels
- 8. If n is not a natural number, then all even numbers can be expressed as____ All odd numbers can be expressed as____ The number divisible by 5 can be expressed as___ The number 2 divided by 3 can be expressed as___ .
- 9. There are () odd numbers between 100 and 200, () even numbers, and () multiples of 5. The ones of 3 can be divided by 3 and 5 at the same time How many can be divided by 3 and 5 at the same time
- 10. If a number can be divisible by two and three at the same time, it must be divisible by six______ ．
- 11. Read the formula "1 + 2 + 3 + 4 +..." 100 "is the sum of 100 consecutive natural numbers starting from 1 as follows It's inconvenient to write. For the sake of simplicity, we express it as ∑ (100 above, n = 1 below, and N on the right). Here the ∑ is the summation sign. Through reading the above materials, we can calculate ∑ {20 above, n = 1 below, and 1 / n (n + 1) on the right}? What does n (n + 1) mean? I don't understand it at all,
- 12. The sum of two natural numbers is 9858. The larger number is equal to the smaller number after removing the single digits. What are the two numbers? One more question: in the sixth grade group, the number of boys accounted for 4 / 9 of the total number of the group. Later, seven boys were transferred in. At this time, the number of boys was just 3 / 5 of the total number of the group? Please, I'm stupid. I have a lot of questions to ask you. Can I help you? Thank you! Another question: there are 120 ball, divided into two classes, class 1 to 3 / 1 and class 2 to 2 / 1 equal, ask two classes each to several ball?
- 13. SOS, known a four digit, thousands, hundreds, tens, and is the complete square of a natural number! Please use C + + program to calculate the number! (in fact, 7744!)
- 14. Take any 11 numbers from 1 to 20 and prove that there must be two numbers, one of which is a multiple of the other
- 15. For three continuous natural numbers, the sum of the square difference of the larger and smaller numbers and the middle natural number must be the multiple of that number? 1,3,4,5
- 16. A natural number plus 1 is a multiple of 2.3.4.5.6.7 A natural number, plus 1, is a multiple of 2 Plus one is a multiple of three Plus one is a multiple of four Plus one is a multiple of five Plus one is a multiple of six Plus one is a multiple of seven What's the number?
- 17. A natural number, it plus L is a multiple of 2, its two times plus 1 is a multiple of 3, its three times plus 1 is a multiple of 5______ ．
- 18. Let a and n be positive integers, and a divide by 2n ^ 2. Try to explain that n ^ 2 + A is not an answer before the square number,
- 19. Primary school mathematics defines "in the natural number, what can be divided by 2 is even, what cannot be divided by 2 is odd". Now it is stipulated that there are odd and even numbers in negative integers
- 20. Let n denote an integer, and use the formula containing n to denote: (1) any even number; (2) any odd number