Addition ShortcutFrom: Anonymous Subject: Math problem Dear Dr. Math, I have a problem that I know how to solve, but I would like to know if there is a shortcut. The problem is: (2+4+6+8+ ... +34)/(3+6+9+12+ ... +54) I solved it by adding all numbers up. Please teach me a proper way of solving this kind of question. Thank you very much, Irene From: Doctor Wilkinson Subject: Re: Math problem Dear Irene, Adding all the numbers up is not stupid. Lot's of people are too lazy to do that much. But I'll show you a clever trick. You want to add: 2 + 4 + 6 + 8 + ... + 34 Do it twice! This gives you: 2 + 4 + 6 + 8 + ... + 34 + 2 + 4 + 6 + 8 + ... + 34 Now reverse the bottom row. This gives you: 2 + 4 + 6 + 8 + ... + 34 + 34 +32 +30 +28 +... + 2 = 36 +36 +36 +36 +... + 36 You have seventeen 36's to add to get twice the sum you want, so the sum is: 17 * 36 / 2 = 17 * 18 I'll let you figure out the sum in the denominator. -Doctor Wilkinson, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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