3)Dr. Strange is more that just the world\'s Sorcerer Supreme; he is also a math

Question

3)Dr. Strange is more that just the world's Sorcerer Supreme; he is also a mathemagician! For his first amazing feat, he will add the first 100 counting numbers for you. Dr. Strange closes his eyes and mumbles a few cryp- tic phrases before confidently stating "5050." The whole process takes him roughly 5 seconds. a) Are you astounded? Why or why not? b) Dr. Strange takes pity on you and invites you to consider the sum of Try to draw your way to the solution. c) Now see if you know how Dr. Strange came up with the answer 5050 for the sum of the first 100 counting numbers. If you do, you probably know how to get the sum of the first 250... d) This one's a bit harder: what about the sum of the squares of the first 100 counting numbers?

Explanation / Answer

(a)Adding First 100 counting numbers is an easy task.

Simply an it forms Arithmetic Progression:

1,2,3,.....100

Sn = (n/2)(a+l) , S100 = (100/2)(1+100) = 50(101) = 5050

(b) sum of first 5 numbers : 1,2,3,4,5

S5 = (5/2)(1+5) = (5/2).6 = 15

(c) sum of first 250 numbers:

S250 = (250/2)(1+250) = (125).251 = 31,375

(d) sum of squares of first 100 numbers:

S = [n(n+1)(2n+1)]/6 = 100(101)(201)/6 = 338,350

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