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saikai
12-10-2004, 07:34 AM
Q1
The sum of positive integers is 1275. What is the sum of integers from 51-100?

Q2
Col A

37*(37/36)

Col B

37 + (37/36)

Thanks in advance.

adonis
12-10-2004, 09:07 AM
Q1 not clear
still,

use sum of AP

S = n/2(2a + (n-1)d)

n - total number of elements( in this case 100 -51 +1 = 50)
a - first element of the series.( in this case 51)
d - common difference( in this case 1)

S = 50/2( 102 + 49) = 25( 151) = 3775.

Another method.

use the sum of 'n' natural nos.

sum of 'n' natural numbers = n(n+1)/2.

Sum of 51 to 100 = Sum of (n from 1 to 100) - Sum of (n from 1 to 50)

(1)Sum of 1 to 100 = 100*101/2 = 5050.
(2)Sum of 1 to 50 = 50*51/2 = 1275.

Sum of 51 to 100 = (1) - (2) = 5050 - 1275 = 3775

Q2

37 + (37/36) = 37 *[ 1+ 1/36] = 37*(37/36)

Both are equal.

Cheers
adonis

saikai
12-10-2004, 10:14 PM
Thank you. Your answers are correct.