What's the Sum?

15 Points Per Correct Answer - No time limit  

1. Which Greek letter is used to denote summation in mathematics? Sigma Epsilon Lambda Alpha

2. Pick any number from 2 to 9. Now, multiply that number by 9. You will get a 2-digit number. Sum up the 2 individual digits and type in your answer. Answer: (A 1-digit number)

3. To determine whether a number can be divided completely by 3 without any remainder, we can sum up their individual digits. If the sum is divisible by 3, then the number itself can also be divisible by 3. Which of the following numbers is NOT divisible by 3? 767676767 998877663 123321333 696222333

4. The sum of the three most beautiful and intriguing mathematical constants, pi, e and Phi is closest to which integer? 9 5 11 7

5. Evaluate the sum of all the positive integers between 1 and 100 (inclusive) that are divisible by 10. 5500 550000 55000 550

6. The sum of the first 10 positive integers, 1 + 2 + … + 9 + 10 is 55. What’s the trick here? Well, notice that 1 + 2 + … + 9 + 10 = 1 + 10 + 2 + 9 +… = (1 + 10) + (2 + 9) + … = 11 + 11 + … = 5 (11) = 55. Now, your turn. What is the sum of the first 1000 positive integers? Answer: (A 6-digit number)

7. Given that the sum of the first 100 odd integers, namely 1 + 3 + … + 197 + 199 = 10000. Now can you tell me what is the sum of the first 100 even integers, namely 2 + 4 + … + 198 + 200? 10100 20100 10000 20000

8. Is the sum of 1 + 2 – 3 + 4 - ... - 97 + 98 – 99 + 100 the same as the sum of 1 – 2 + 3 – 4 ... + 97 – 98 + 99 – 100? Yes No

9. By using the partial fraction technique, the fraction 1/[(n)(n+1)] can be rewritten as 1/n – 1/(n+1). For example, 1/(2x3) = 1/6 is equivalent to 1/2 - 1/3. What is the sum of 1/2 + 1/6 + 1/12 + … + 1/9702 + 1/9900 = 1/(1x2) + 1/(2x3) + 1/(3x4) + … + 1/(98x99) + 1/(99x100)? 0.99 0.95 0.97 0.93

10. A = the number of sides of a pentagon; B = the third odd positive integer; C = the fifth Fibonacci number (the sequence starts with 1, 1, 2…); D = the number of diagonals of a pentagon; E = the third prime number. What is the sum of A, B, C, D and E? In other words, compute A + B + C + D + E. Answer: (A 2-digit number)