(7²+1)/(7²-1)+(9²+1)/(9²-1)+…+(99²+1)/(99²-1)简便运算 急

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(7²+1)/(7²-1)+(9²+1)/(9²-1)+…+(99²+1)/(99²-1)简便运算急(7²+1)/(7²

(7²+1)/(7²-1)+(9²+1)/(9²-1)+…+(99²+1)/(99²-1)简便运算 急
(7²+1)/(7²-1)+(9²+1)/(9²-1)+…+(99²+1)/(99²-1)简便运算 急

(7²+1)/(7²-1)+(9²+1)/(9²-1)+…+(99²+1)/(99²-1)简便运算 急

(7²+1)/(7²-1)+(9²+1)/(9²-1)+…+(99²+1)/(99²-1)
=[1+2/(7²-1)]+[1+2/(9²-1)]+[1+2/(11²-1)]+……+[1+2/(99²-1)]
=1+2/(7+1)(7-1)+1+2/(9+1)(9-1)+1+2/(11+1)(11-1)+……+1+2/(99+1)(99-1)
=1×47+2/6*8+2/8*10+2/10*12+……+2/98*100 (有47个1相加)
=47+(1/6-1/8+1/8-1/10+……+1/98-1/100)
=47+1/6-1/100
=47+94/600
=47又47/300 (47又300分之47)