奥数题2/(2+5)+2/(5+8)+2/(8+11)+.+2/(2003+2006)+2/(2006+2009)怎么做括号内是分母,中间是加号
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 16:14:41
![奥数题2/(2+5)+2/(5+8)+2/(8+11)+.+2/(2003+2006)+2/(2006+2009)怎么做括号内是分母,中间是加号](/uploads/image/z/7104296-56-6.jpg?t=%E5%A5%A5%E6%95%B0%E9%A2%982%2F%282%2B5%29%2B2%2F%285%2B8%29%2B2%2F%288%2B11%29%2B.%2B2%2F%282003%2B2006%29%2B2%2F%EF%BC%882006%2B2009%EF%BC%89%E6%80%8E%E4%B9%88%E5%81%9A%E6%8B%AC%E5%8F%B7%E5%86%85%E6%98%AF%E5%88%86%E6%AF%8D%EF%BC%8C%E4%B8%AD%E9%97%B4%E6%98%AF%E5%8A%A0%E5%8F%B7)
奥数题2/(2+5)+2/(5+8)+2/(8+11)+.+2/(2003+2006)+2/(2006+2009)怎么做括号内是分母,中间是加号
奥数题2/(2+5)+2/(5+8)+2/(8+11)+.+2/(2003+2006)+2/(2006+2009)怎么做
括号内是分母,中间是加号
奥数题2/(2+5)+2/(5+8)+2/(8+11)+.+2/(2003+2006)+2/(2006+2009)怎么做括号内是分母,中间是加号
2/(2*5)+2/(5*8)+2/(8*11)+.+2/(2003*2006)+2/(2006*2009)
=2/3(1/2-1/5+1/5-1/8+1/8-1/11+.+1/2003-1/2006+1/2006-1/2009)
=2/3(1/2-1/2009)
=1/3-2/6027
=2007/6027
括号中都是分母么?
解释一下,括号内是分母还是分子,OK?
至少说清楚
2/(2+5)+2/(5+8)+2/(8+11)+......+2/(2003+2006)+2/(2006+2009)
=2*(2+5+5+8+8+8+11+11+......+2003+2006+2006+2009)
=2*[2+2009+2*(5+8+11+......+2003+2006)]
=2*{2+2009+2*[(2006+5)*668÷2]}
=2690718
>2.28764
你确定是加号?如果是的话分母是6n+1,吧这个数列和当成级数x^(6n+1)/(x*(6n+1))的和,然后把x提到求和符号外面,在求一次导就可以出来了。。不过这样挺复杂,是2*5吧?
前一项比后一项大12 除第一项 后面的提出12 里面的倒序相加即可
原式=2/3×(1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14……+1/2003-1/2006+1/2006-1/2009)
=2/3×(1/2-1/2009)
=2/3×2007/5008
=669/2009