(1/1×4)+(1/4×7)+(1/7×10)+…+(1/97×100) 1×4,4×7那些是分母。 只需要化簡就好，謝謝?

1/(1*4) + 1/(4*7) + 1/(7*10) + ...... + 1/(94*97) + 1/(97*100)
= (1/3)( 1/1 - 1/4 ) + (1/3)( 1/4 - 1/7 ) + (1/3)( 1/7 - 1/10 ) + ...... + (1/3)( 1/94 - 1/97 ) + (1/3)( 1/97 - 1/100 )
= (1/3)( 1/1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ...... + 1/94 - 1/97 + 1/97 - 1/100 )
= (1/3)( 1/1 - 1/100 )
= (1/3)( 1 - 0.01 )
= (1/3) * 0.99
= 0.33 ..... Ans

0.33