- #1
hadi amiri 4
- 98
- 1
find the sum
(1/4!)+(4!/8!)+(8!/12!)+...
(1/4!)+(4!/8!)+(8!/12!)+...
Not so!daudaudaudau said:That is clearly divergent. Try to simplify it and you will see.
mathman said:Not so!
An upper bound would be 1 + 1/5^4 + 1/9^4 + 1/13^4 + ... which converges.
hadi amiri 4 said:the answer contains Pi and Ln .
hadi amiri 4 said:[tex] \sum _{k=0}^\infty \frac{1}{(4k+1)(4k+2)(4k+3)(4k+4)}[/tex]
The sum of the given fractions is 17/12 or 1.4166 when rounded to four decimal places.
To find the sum of fractions with different denominators, you need to first find a common denominator. This can be done by finding the least common multiple (LCM) of the denominators. Then, convert each fraction to an equivalent fraction with the common denominator and add them together. In this case, the LCM of 4, 8, and 12 is 24, so we convert 1/4 to 6/24, 4/8 to 12/24, and 8/12 to 16/24. The sum is then 34/24 which simplifies to 17/12.
Yes, the sum of fractions with different denominators can be simplified if possible. In this case, we can simplify 17/12 to 1.4166 by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case.
Yes, there is a formula for finding the sum of fractions with different denominators. It is: Sum = (a/b) + (c/d) + (e/f) + ... = (ad + bc + ef + ...) / (bd * df * ...)
Yes, it is possible to find the sum of fractions without converting them to equivalent fractions. This can be done by using the formula mentioned in the previous answer. However, converting them to equivalent fractions makes the calculation easier and reduces the chance of error.