21分之1+77分之1+165分之1+285分之1+437分之1
问题描述：
21分之1+77分之1+165分之1+285分之1+437分之1
答
21分之1+77分之1+165分之1+285分之1+437分之1
=1/3x7+1/7x11+1/11x15+1/15x19+1/19x23
=1/4[1/3-1/7]+1/4[1/7-1/11]+...+1/4[1/19-1/23]
=1/4[1/3-1/23]
=1/4*20/69
=5/69
答
1/21+1/77+1/165+1/285+1/437
=1/(3*7)+1/(11*7)+1/(11*15)+1/(15*19)+1/(19*23)
=1/4*[(1/3-1/7)+(1/7-1/11)+(1/11-1/15)+(1/15-1/19)+(1/19-1/23)]
=1/4*(1/3-1/23)
=1/4*(20/69)
=5/69
答
21分之1+77分之1+165分之1+285分之1+437分之1
=（1/3-1/7+1/7-1/11+1/11-1/15+1/15-1/19+1/19-1/23）÷4
=（1/3-1/23）÷4
=20/69÷4
=5/69