化简:(1/√2+√4)+(1/√4+√6)+……+(1/(√2n-2)+(√2n))(n为正整数,且n≠2)RT,化简:(1/√2+√4)+(1/√4+√6)+……+(1/(√2n-2)+(√2n))(n为正整数,且n≠2)坐等.
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![化简:(1/√2+√4)+(1/√4+√6)+……+(1/(√2n-2)+(√2n))(n为正整数,且n≠2)RT,化简:(1/√2+√4)+(1/√4+√6)+……+(1/(√2n-2)+(√2n))(n为正整数,且n≠2)坐等.](/uploads/image/z/1259200-64-0.jpg?t=%E5%8C%96%E7%AE%80%EF%BC%9A%281%2F%E2%88%9A2%2B%E2%88%9A4%29%2B%281%2F%E2%88%9A4%2B%E2%88%9A6%29%2B%E2%80%A6%E2%80%A6%2B%281%2F%28%E2%88%9A2n-2%29%2B%28%E2%88%9A2n%29%29%28n%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0%2C%E4%B8%94n%E2%89%A02%29RT%2C%E5%8C%96%E7%AE%80%EF%BC%9A%281%2F%E2%88%9A2%2B%E2%88%9A4%29%2B%281%2F%E2%88%9A4%2B%E2%88%9A6%29%2B%E2%80%A6%E2%80%A6%2B%281%2F%28%E2%88%9A2n-2%29%2B%28%E2%88%9A2n%29%29%28n%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0%2C%E4%B8%94n%E2%89%A02%29%E5%9D%90%E7%AD%89.)
化简:(1/√2+√4)+(1/√4+√6)+……+(1/(√2n-2)+(√2n))(n为正整数,且n≠2)RT,化简:(1/√2+√4)+(1/√4+√6)+……+(1/(√2n-2)+(√2n))(n为正整数,且n≠2)坐等.
化简:(1/√2+√4)+(1/√4+√6)+……+(1/(√2n-2)+(√2n))(n为正整数,且n≠2)
RT,化简:(1/√2+√4)+(1/√4+√6)+……+(1/(√2n-2)+(√2n))(n为正整数,且n≠2)
坐等.
化简:(1/√2+√4)+(1/√4+√6)+……+(1/(√2n-2)+(√2n))(n为正整数,且n≠2)RT,化简:(1/√2+√4)+(1/√4+√6)+……+(1/(√2n-2)+(√2n))(n为正整数,且n≠2)坐等.
(1/√2+√4)+(1/√4+√6)+……+(1/(√2n-2)+(√2n))
=(√2-√4)/[(√2+√4)(√2-√4)]+(√4-√6)/[(√4+√6)(√4-√6)]+
……+(√2n-2-√2n)/[(√2n-2+√2n)(√2n-2-√2n)]
=(√2-√4)/(-2)+(√4-√6)/(-2)+……+(√2n-2-√2n)/(-2)
=(-½)×(√2-√4+√4-√6+……+√2n-2-√2n)
=(-½)×(√2-√2n)
先看最后一项1/(√2n-2)+(√2n))
分子分母同时乘(√2n)-(√2n-2))
得分子:(√2n)-(√2n-2))
分母:2
所以提出公因式1/2
(1/√2+√4)+(1/√4+√6)+……+(1/(√2n-2)+(√2n))
=(1/2)(√4-√2 +.........+(√2n)-(√2n-2))
=(1/2) (-√2+√2n)
[(√2n-2)+(√2n)][(-√2n-2)+(√2n)]=2n-(2n-2)=2
所以1/(√2n-2)+(√2n)=[(-√2n-2)+(√2n)]/2
所以
(1/√2+√4)+(1/√4+√6)+……+(1/(√2n-2)+(√2n))
=(-√2+√4)/2+(-√4+√6)/2+……+[(-√2n-2)+(√2n)]/2
=(-√2+√2n)/2
1/(√2n-2)+(√2n)=-(√2n-2+√2n)/2
(1/√2+√4)+(1/√4+√6)+……+(1/(√2n-2)+(√2n))
=(-√2+√4-√4+√6+……-√2n-2+√2n)/2
=(√2n-√2 )/2