The difference of the reciprocals of two consecutive integers is 1/72. Find the smaller of the two integers.

The difference of the reciprocals of two consecutive integers is 1/72. Find the smaller of the two integers.

unknown values: n

equation: 1/n - 1/(n+1) = 1/72

answer: -9 or 8

the square root of the sum of two consecutive integers is equal to 9. find the smaller integer

unknown values: x

equation: (x+x+1)^(1/2)=9

answer: 40

Finding the sum of series. 3+6+12+24+...+384?

unknown values: s

equation: 3*2^(n-1) = 384

equation: s = 3*(2^n-1)/(2-1)

answer: 765

When the reciprocal of 4 times a number is subtracted from 2, the result is twice the reciprocal of the number. Find the number.

unknown values: x

equation: 2- 1/(4*x) = 2/x

answer: 9/8 | 1.125

The number A = 200420052006....2040 is formed by putting the consecutive integers from 2004 to 2040 together.What is the remainder when A is divided by 9?

unknown values: r

equation: s = (2004+2040)(2040-2004+1)/2

equation: r = s % 9

answer: 6

The digits of a three digit number are consecutive integers. When the digits are reversed the resulting number is 198 larger that the original number. If the original number is an integral multiple of 7, what is the original number?

unknown values: n

equation: n = 100*a+10*b+c

equation: 100*c+10*b+c = 198 + n

equation: b = a+1

equation: c = b+1

equation: n%7=0

answer: 567

The numerator of a fraction is 5 less than the denominator. If 1 is added to both the numerator and the denominator the fraction would become 2/3. Find the fraction.

unknown values: f

equation: f = n/d

equation: n = d - 5

equation: (n+1)/(d+1) = 2/3

answer: 9/14

The sum of the reciprocals of two consecutive odd integers is 8/15. Find the integers.

unknown values: 2*n+1,2*n+3

equation: 1/(2*n+1) + 1/(2*n+3) = 8/15

equation: is_integer(n)

answer: 3; 5

The sum of 4 consecutive odd integers is 3 more than 5 times the least of the integers. Find the integers.

unknown values: m, n, x, y

equation: m % 2 = 1

equation: m + 2 = n

equation: n + 2 = x

equation: x + 2 = y

equation: m + n + x + y = 3 + 5*m

answer: 9; 11; 13; 15

What number can be subtracted from both the numerator and the denominator of 17/25 to form a fraction equal to 3/5?

unknown values: n

equation: (17-n)/(25-n) = 3/5

answer: 5