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1/1x3x5+1/3x5x7+1/5x7x9……1/95x97x99
如题所述
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其他回答
第1个回答 2022-08-21
an=1/[(2n-1)(2n+1)(2n+3)]=(1/4) { 1/[(2n-1)(2n+1)] -1/[(2n+1)(2n+3)] }Sn =a1+a2+...+an1/(1x3x5)+1/(3x5x7)+1/(5x7x9)+...+1/(95x97x99)=S48= (1/4) ( 1/(1x3) - 1/(97x99)]= (1/4) (1/3 - 1/9603]=800/9603
相似回答
1/
1x3x5+1
/
3x5x7+1
/
5x7x9……1
/
95x97x99
答:
an=1/[(2n-1)(2n+1)(2n+3)]=(1/4) { 1/[(2n-1)(2n+1)] -1/[(2n+1)(2n+3)] }Sn =a1+a2+...+an1/(
1x3x5
)+1/(
3x5x7
)+1/(
5x7x9
)+...+1/(
95x97x99
)=S48= (1/4) ( 1/(1x3) - 1/(97x99)]= (1/4) (1/3 - 1/9603]=800/9603 ...
1/
1x3x5+1
/
3x5x7+1
/
5x7x9……1
/
95x97x99
答:
也就是说:1/
1x3x5
=1/8[1/1-2/3+1/5]1/
3x5x7
=1/8[1/3-2/5+1/7]
……1
/
95x97x99
=1/8[1/95-2/97+1/99]相加的时候,写成竖式更容易看出来结果为 =1/8[1-1/3-1/97+1/99]
1/
1x3x5+1
/
3x5x7+1
/
5x7x9
+.+1/2003x2005x2007
答:
分析:1/1x3x5=1/4×(1/1*3 -1/3*5) 1/
3x5x7
=1/4×(1/3*5 -1/5*7) 1/
5x7x9
=1/4×(1/5*7 - 1/7*9) 1/7*9*11=1/4×(1/7*9 -1/9*11) .1/2003x2005x2007=1/4×(1/2003*2005 -1/2005*207) 所有的等式相加有 1/
1x3x5+1
/3x5x...
奥数题1/
1x3x5+1
/
3x5x7+1
/
5x7x9……1
/
97x99
x101
答:
设通项为1/(n-2)n(n+2) 可以化为1/8(1/(n-2)-2/n+1/(n+2)) 裂项求和即可。
1x3
x1/5+
3x5
×7/
1+
答:
1/(
1x3x5
)+1/(
3x5x7
)+...+1/(
95x97x99
)=1/4x【1/(1x3)-1/(3x5)+1/(3x5)-1/(5x7)+...+1/(95x97)-1/(97x99)】= 1/4x 【 1/(1x3) - 1/(97x99)】= 1/4x (1/3 - 1/9603)=800/9603
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