(22+1/22-1 ) + (32+1/32-1) + (42+1/4-21 )+......+ ( n2+1/n2-1 )= ?
用含n的代数式表示
(22+1/22-1 ) + (32+1/32-1) + (42+1/4-21 )+......+ ( n2+1/n2-1 )= ?
用含n的代数式表示
n ²+ 1/n ²-1= 1+ 2/n ²-1 =1+ 1/n-1 -1/n+1则 (22+1/22-1 ) + (32+1/32-1) + (42+1/4-21 )+......+ ( n2+1/n2-1 )= (1+1-1/3)+(1+1/2-1/4)+(1+1/3-1/5)+...+1+ 1/n-1- 1/n+1= n+1+1/2-1/n+1- 1/n=n+ 3/2- 1/n+1- 1/n