Oh honey, that's an easy one. The sum of all numbers between 1000 and 2000 is 1,499,500. Just add 1000 and 2000, divide by 2 to get the average (1500), then multiply by the number of terms (1000) and you're good to go. Math doesn't have to be a headache, darling.
All numbers between 1000 and 2000, or anywhere else, can be expressed as a power of another number.
3 integers: 1200,1500,1800
1001,1111,1221,1331,1441,1551,1661,1771,1881,1991,2002,2112,2222,2332,2442,2552,2662,2772,2882,2992,3003,3113,3223,3333,3443,3553,3663,3773,3883,3993,4004,4114,4224,4334,4444,4554,4664,4774,4884,4994: 40 numbers in all.
All the odd numbers between 1 and 2001.
All numbers that are divisible by 5 and 9 are multiples of their lcm which is 45. So the question boils down to which multiples of 45 are between 1000 & 2000. 1000 ÷ 45 = 222/9 2000 ÷ 45 = 444/9 Thus the solution is the multiples of 45 from 23 to 44 which are: 1035, 1080, 1125, 1170, 1215, 1260, 1305, 1350, 1395, 1440, 1485, 1530, 1575, 1620, 1665, 1710, 1755, 1800, 1845, 1890, 1935, 1980
All numbers between 1000 and 2000, or anywhere else, can be expressed as a power of another number.
-1000
3 integers: 1200,1500,1800
They are all the 4 digit numbers starting with 1 and ending with 1, 3, 5, 7 or 9. Since there are 500 of them, I will not list them.
A palindromic number is a number that remains the same when its digits are reversed. Between 1000 and 2000, the possible palindromic numbers have the form "ABBA" where A and B are digits from 1 to 9. There are 9 options for A (1-9) and 10 options for B (0-9), but we exclude the case where A is 0. Therefore, there are 9 * 10 = 90 palindromic numbers between 1000 and 2000.
1001,1111,1221,1331,1441,1551,1661,1771,1881,1991,2002,2112,2222,2332,2442,2552,2662,2772,2882,2992,3003,3113,3223,3333,3443,3553,3663,3773,3883,3993,4004,4114,4224,4334,4444,4554,4664,4774,4884,4994: 40 numbers in all.
1 to 999
All the odd numbers between 1 and 2001.
All of them.
The sum of all the integers between 1,000 and 2,000 is 1,498,500.
500
The sum of all numbers between 1 and n = n*(n+1)/2 The sum of all numbers between 1 and 999 = 999*1000/2 = 499500 The sum of all numbers between 1 and 9999 = 9999*10000/2 = 49995000 So, the sum of all numbers between 1000 and 9999 = 49495500