A student finds the sum 1 + 2 + 3 + ... as his patience runs out. He found the sum as 575. When the teacher declared the result wrong, the student realized that he missed a number. What was the number the student missed?
Explanation:
Sum of first n natural numbers = S(n)
Sum given by student = 575
S(10) = 10×112 = 55
S(20) = 20×212= 210
S(30) = 30×312= 465
S(40) = 40×412= 820
∴ The student stopped counting somewhere between 30 and 40.
Consider S(35) = 36×352= 630
The student stopped somewhere before 35.
∴ S(31) = 496, S(32) = 528, S(33) = 561 and S(34) = 595
But the student gave 575 as the sum, so the student missed on the number 20.
Hence, option (d).
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