1/1*5+1/3*7+1/5*9+.+1/(2n-1)(2n+3)
1/1*5+1/3*7+1/5*9+.+1/(2n-1)(2n+3)
=【(1-1/5+1/3-1/7+1/5-1/9+.+1/(2n-1)-1/(2n+3) 】÷4
=【1+1/3-1/(2n+1)-1/(2n+3)】÷4
=1/3-(n+1)/[(2n+1)(2n+3)]
RELATED INFORMATIONS
- 1. 1+3+5+7… +(2n-1)=______ (denoted by the formula containing N, where n = 1, 2, 3 .)
- 2. Calculate 1 / (1 * 3) + 1 / (3 * 5) + 1 / (5 * 7) +... + 1 / (2n-1) * (2n-1) =?
- 3. In fact, just find the rules A diamond with a side length of 1 and an angle of 60 degrees, whose height is the side of the second diamond, is still a diamond with an angle of 60 degrees?
- 4. A set of formulas in regular order: The third power of a is the fifth power of B, the third power of a is the eighth power of B, A to the fourth power, B to the eleventh power (AB ≠ 0), where the seventh formula is______ . The nth formula is_______ (n is a positive integer) Change "the third power of a to the fifth power of B" to "the second power of a to the fifth power of B" The first floor is obviously wrong.
- 5. Find the rule: 27 0 () 0 () The sum is 27, (), () Using quadratic function to solve the problem···
- 6. Lim x tends to 0 (x-sin x) / x ^ 3
- 7. How to do LIM (x → 0) (TaNx SiNx) / (X & # 179;)
- 8. (2 and one seventh) - (- 5 and one third) - (+ 3 and one seventh) - (- 3 and two thirds) how to do it, -15 1 / 3 - (3 1 / 7) - 4 2 / 3 - (8 1 / 7) - 0.5 - (3 and a quarter) + 2.75 - (7 and a half)
- 9. Calculation. 199 + 299 + 399 + +29699
- 10. One plus two plus three plus four plus five. How much is 99 plus 100?
- 11. 3+5+7+9… +(2n-1)+(2n+1)=
- 12. 16,23,9,30,2, () to find the law needs method
- 13. ,13,37,109,( ),( )
- 14. Fill in the blanks: 1,1,2,3,7,16,65_ ,4546,……
- 15. How to fill in the brackets?
- 16. Find the rule, 16,3.8,9,4. {}, {}. What's in the brackets
- 17. Find the law, 1 / 2, 1 / 3, 1 / 10, 1 / 15, 1 / 26. The ninth number is Fast
- 18. 2 / 3,1 has 1 / 3,2,1 has 2 / 3,3 has 1 / 3,4, (), () find the difference between the 100th and 50th numbers
- 19. Find the rule and add the number 1,8,27,( ),125,216,. There are also 12 / () = 0.75 = 24 / 24 () = (); 4 = ()% as required, so that their greatest common factor is 1 1. Both books are prime numbers; () and () 2. Both books are composite numbers; () and (). 3 are prime numbers and composite numbers; () and ()
- 20. Find the rule and add the number 3,9,17,19,(