1/1x3=1/2(1-1/3),1/3x5=1/2(1/3-1/5),1/5x7=1/2(1/5-1/7),……,1/17x19=1/2(1/17-1/19).∴1/1x3+1/3x5+1/5x7+……+1/17x19=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+……+1/2(1/17-1/19)=1/2 (1-1/3+1/3-1/5+1/5-1/7+……+1/17-1/19)=1/2(1-1/19)=9/19根据以上材料,回答下列问题:(1)在式子1/1x3+1/3x5+1/5x7+……中第五项是________(2)写出第n个 等式,并证明(3)当m=4时计算1/m(m+4)=1/(m+4)(m+8)+.+1/(m+92)(m+96)的值
问题描述:
1/1x3=1/2(1-1/3),1/3x5=1/2(1/3-1/5),1/5x7=1/2(1/5-1/7),……,1/17x19=1/2(1/17-1/19).∴1/1x3+1/3x5+1/5x7+……+1/17x19
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+……+1/2(1/17-1/19)
=1/2 (1-1/3+1/3-1/5+1/5-1/7+……+1/17-1/19)
=1/2(1-1/19)
=9/19
根据以上材料,回答下列问题:
(1)在式子1/1x3+1/3x5+1/5x7+……中第五项是________
(2)写出第n个 等式,并证明
(3)当m=4时计算1/m(m+4)=1/(m+4)(m+8)+.+1/(m+92)(m+96)的值
答