Question

1*3*5分之1 +3*5*7分之1+5*7*9分之1•••••••+11*13*15分之1=?

Answer 1

1*3*5分之1 +3*5*7分之1+5*7*9分之1•••••••+11*13*15分之1
=1/4[1/(1×3)-1/(3×5)+1/(3×5)-1/(5×7)+...+1/(11×13)-1/(13×15)]
=1/4[1/(1×3)-1/(13×15)]
=1/4×64/195
=16/195

Answer 2

1/[(n-2)n(n+2)]=[n²+2n)+(n²-2n)-2(n²-4)]/8/[(n-2)n(n+2)]
= [1/(n-2) + 1/(n+2) - 2/n ] /8

1/(1*3*5)+1/(3*5*7)+1(5*7*9)+1/(7*9*11)+1(9*11*13)+1/(11*13*15)
={(1/1+1/5- 2/3)+ (1/3+1/7- 2/5) + (1/5+1/9- 2/7) + (1/7+1/11- 2/9)+(1/9+1/13- 2/11)+ (1/11+1/15- 2/13}/8
= (1- 1/3 - 1/13 + 1/15)/8
= 16/195

Answer 3

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