2楼小甲虫妈妈V1.0
(爱学习的虫子)
发表于 2007-11-1 23:07
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(3² + 1) / ( 3² -1) +( 5² +1 ) / (5²-1)+ (7²+1) / (7²- 1)+ (9²+1) / (9²-1)+ (11²+1) / (11²-1)+ (13²+1) / (13²-1)+(15²+1) / (15²-1)+(17 ²+1) / (17²-1)+(19²+1) / (19²-1)
=(3² - 1+2) / ( 3² -1)+ ( 5² -1+2 ) / (5²-1) +(7²-1+2) / (7²- 1)+……(17 ²-1+2) / (17²-1)+(19²-1+2) / (19²-1)
=(1+2 / ( 3² -1))+(1+2 / (5²-1)) +(1+2 / (7²-1))+ ……+(1+2 / (17²-1)) +(1+2 / (19²-1))
=9+2 / ( 3² -1) +2 / (5²-1) +2 / (7²-1) + ……+2 / (17²-1) +2 / (19²-1)
=9+2/(2x4)+2/(4x6)+2/(6x8)+……+2/(16x18)+2/(18x20)
=9+(1/2-1/4+1/4-1/6+1/6-1/8+……+1/16-1/18+1/18-1/20)
=9+1/2-1/20
=189/20.
