How to sum 1 / 1 * 3 + 1 / 3 * 5 + '+ 1 / (2n-1) (2n + 1) with split term method?
1/1*3+1/3*5+...+1/(2n-1)(2n+1)
=1-2/3+2/3-3/5+3/5-4/7+...+n/(2n-1)-(n+1)/(2n+1)
=1-(n+1)/(2n+1)
n/(2n+1)
RELATED INFORMATIONS
- 1. BN = 1 / (2n-1) (2n) sum
- 2. How to sum BN = 1 / [2n]
- 3. Sum of split terms 1 / (3 ^ 2-1) + 1 / (5 ^ 2-1) + 1 / (7 ^ 2-1) + .+ 1/[(2n+1)^2 -1] + … ..=
- 4. Sum function of power series (∞Σn = 0) {((- 1) ^ n) * (x ^ 2n)} / N~
- 5. A = 9, B = - 8, then the 2003 power of a + the 2004 power of B is
- 6. What is the single digit number of 3 to the power of 2007
- 7. The 5th power of 2 = 32, the 6th power of 2 = 64, the 7th power of 2 = 128. Write the 32-bit number of 2 according to the law, and the number of the 2007 power of 3 is
- 8. How to add the first power of 15 to the second power of 15 and the third power of 15 to the 100th power of 15
- 9. What are the last two digits of 101 to the power of 2010 + 25 to the power of 2010? Please make it clear,
- 10. Given a + B-8A + 6B + 25 = 0, find the value of a + ab-6 of a-4ab + 4b, and the value of a + ab-6 of a + 4B How can elder martial brothers and sisters help My problem will be taught tomorrow!
- 11. The shape of a cell in the human body can be approximately seen as a circle. It is known that its diameter is about 1.56 * 10-6 cubic meters, then its one millionth is () meters
- 12. Given a = a ^ 2-2ab + B ^ 2, B = a ^ 2 + 2Ab + B ^ 2.1: find a + B 2: find a quarter (B-A) 3: if 2a-3b + C = 0, then what is the expression of C?
- 13. How many jin is a liter of diesel? How to convert? How to convert gasoline?
- 14. Any sufficiently large even number can be expressed as the product of a prime number and two prime numbers For example: 8 = 2 + 2 × 3, then: 54 = () + () × () 144 = () + () × ()
- 15. How to write it (all) from Peking University Teacher's edition, I've written it myself, I didn't look at it carefully at first. I thought it was very difficult
- 16. B / a = 3, what is the cubic power of B / a
- 17. White, black, white, black, black. Where are the sixth and tenth white balls?
- 18. The summary of physics knowledge in the eighth grade volume II of people's Education Press It must be the second volume of the eighth grade
- 19. Given that the derivative of the function f (x) is f '(x) = 4 & sup3; x-4x, and the image passes through the point (0,3), when the function f (x) reaches the minimum, the value of X should be?
- 20. AB is a sequence of numbers. When a equals 3 579, B is 5 913 17. When a equals 117, how much is B