Sum of split terms 1 / (3 ^ 2-1) + 1 / (5 ^ 2-1) + 1 / (7 ^ 2-1) + .+ 1/[(2n+1)^2 -1] + … ..=

It's a test
Considering the characteristics of denominator, (2n + 1) ^ 2-1 = [(2n + 1) - 1] [(2n + 1) + 1] = 4N (n + 1)
And 1 / N (n + 1) = 1 / n-1 / (n + 1)
The final result is n / 4 (n + 1)

RELATED INFORMATIONS

1. Sum function of power series (∞Σn = 0) {((- 1) ^ n) * (x ^ 2n)} / N~
2. A = 9, B = - 8, then the 2003 power of a + the 2004 power of B is
3. What is the single digit number of 3 to the power of 2007
4. 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
5. 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
6. What are the last two digits of 101 to the power of 2010 + 25 to the power of 2010? Please make it clear,
7. 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!
8. Given a + B-8A + 6B + 25 = 0, find the value of a + ab-6 of a-4ab + 4B
9. Given a + B-8A + 6B + 25 = 0, find the solution of a + B of a-4ab + 4B
10. Given a & # 178; + B & # 178; - 8A + 6B + 25 = 0, find a & # 178; - 4AB + 4B & # 178; divided into a & # 178; + ab-6b & # 178; We need to simplify the fraction first
11. How to sum BN = 1 / [2n]
12. BN = 1 / (2n-1) (2n) sum
13. How to sum 1 / 1 * 3 + 1 / 3 * 5 + '+ 1 / (2n-1) (2n + 1) with split term method?
14. 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
15. 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?
16. How many jin is a liter of diesel? How to convert? How to convert gasoline?
17. 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 = () + () × ()
18. 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
19. B / a = 3, what is the cubic power of B / a
20. White, black, white, black, black. Where are the sixth and tenth white balls?