Table of Contents
- 1 What is the minimum sum of any positive number and its reciprocal?
- 2 What is the sum of a number and its reciprocal What is the product of a number and its reciprocal?
- 3 What is the maximum value when a negative number is added to its reciprocal?
- 4 Can the sum of a number and its reciprocal be 2 3?
- 5 How do you find the reciprocal of a reciprocal table?
What is the minimum sum of any positive number and its reciprocal?
The smallest sum of a number n and its reciprocal 1n is 2 which occurs when n=1 . Any other value of n will produce a larger sum.
What is the sum of a number and its reciprocal What is the product of a number and its reciprocal?
1
The reciprocal or multiplicative inverse of a number x is the number which, when multiplied by x , gives 1 . So, the product of a number and its reciprocal is 1 . (This is sometimes called the property of reciprocals .)
What is the only number that when added to its reciprocal is equal to 2?
Using reciprocals
| 4 | ÷ | = |
|---|---|---|
| 5 |
What happens to the sum of the reciprocals of the positive integers if you continue adding them?
If infinitely many numbers have their reciprocals summed, generally the terms are given in a certain sequence and the first n of them are summed, then one more is included to give the sum of the first n+1 of them, etc.
What is the maximum value when a negative number is added to its reciprocal?
1 Expert Answer f(x) = x + 1/x function to be maximized, for x < 0. f'(x) = 1 – x-2; setting this to zero means 1 = 1/x2 and thus x = -1.
Can the sum of a number and its reciprocal be 2 3?
no real number exists for which sum of the number and its reciprocal is 2/3.
What are three consecutive positive integers?
Explanation: Three consecutive even integers can be represented by x, x+2, x+4. The sum is 3x+6, which is equal to 108. Thus, 3x+6=108.
What is the sum of a number and its negative?
The sum of a number and its negative is always 0.
How do you find the reciprocal of a reciprocal table?
To find the reciprocal of any number, just calculate “1 ÷ (that number).” For a fraction, the reciprocal is just a different fraction, with the numbers “flipped” upside down (inverted). For instance, the reciprocal of 3/4 is 4/3. Any number times its reciprocal will give you 1.