数学题,在下面,速度!都要简便计算!谢谢(1)9999×2222+3333×3334(2)1+1/2+2/2+1/3+2/3+3/3+1/4+2/4+3/4+4/4+……+1/100+2/100+……+100/100(3)1/2+1/4+1/8+1/16+1/32+1/64(4)1/1×2×3+1/2×3×4+1/3×4×5+……+1/98×99×100
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 13:39:17
![数学题,在下面,速度!都要简便计算!谢谢(1)9999×2222+3333×3334(2)1+1/2+2/2+1/3+2/3+3/3+1/4+2/4+3/4+4/4+……+1/100+2/100+……+100/100(3)1/2+1/4+1/8+1/16+1/32+1/64(4)1/1×2×3+1/2×3×4+1/3×4×5+……+1/98×99×100](/uploads/image/z/442256-32-6.jpg?t=%E6%95%B0%E5%AD%A6%E9%A2%98%2C%E5%9C%A8%E4%B8%8B%E9%9D%A2%2C%E9%80%9F%E5%BA%A6%21%E9%83%BD%E8%A6%81%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%21%E8%B0%A2%E8%B0%A2%EF%BC%881%EF%BC%899999%C3%972222%2B3333%C3%973334%EF%BC%882%EF%BC%891%2B1%2F2%2B2%2F2%2B1%2F3%2B2%2F3%2B3%2F3%2B1%2F4%2B2%2F4%2B3%2F4%2B4%2F4%2B%E2%80%A6%E2%80%A6%2B1%2F100%2B2%2F100%2B%E2%80%A6%E2%80%A6%2B100%2F100%EF%BC%883%EF%BC%891%2F2%2B1%2F4%2B1%2F8%2B1%2F16%2B1%2F32%2B1%2F64%EF%BC%884%EF%BC%891%2F1%C3%972%C3%973%2B1%2F2%C3%973%C3%974%2B1%2F3%C3%974%C3%975%2B%E2%80%A6%E2%80%A6%2B1%2F98%C3%9799%C3%97100)
数学题,在下面,速度!都要简便计算!谢谢(1)9999×2222+3333×3334(2)1+1/2+2/2+1/3+2/3+3/3+1/4+2/4+3/4+4/4+……+1/100+2/100+……+100/100(3)1/2+1/4+1/8+1/16+1/32+1/64(4)1/1×2×3+1/2×3×4+1/3×4×5+……+1/98×99×100
数学题,在下面,速度!都要简便计算!谢谢
(1)9999×2222+3333×3334
(2)1+1/2+2/2+1/3+2/3+3/3+1/4+2/4+3/4+4/4+……+1/100+2/100+……+100/100
(3)1/2+1/4+1/8+1/16+1/32+1/64
(4)1/1×2×3+1/2×3×4+1/3×4×5+……+1/98×99×100
数学题,在下面,速度!都要简便计算!谢谢(1)9999×2222+3333×3334(2)1+1/2+2/2+1/3+2/3+3/3+1/4+2/4+3/4+4/4+……+1/100+2/100+……+100/100(3)1/2+1/4+1/8+1/16+1/32+1/64(4)1/1×2×3+1/2×3×4+1/3×4×5+……+1/98×99×100
(1)9999×2222+3333×3334
=3333x2222x3+3333x3334
=3333x(6666+3334)
=3333x10000
=33330000
(2)1+1/2+2/2+1/3+2/3+3/3+1/4+2/4+3/4+4/4+……+1/100+2/100+……+100/100
因为1+2+3+……+n-1+n=n(n+1)/2
所以1/n+2/n+3/n+……+n-1/n+n/n=n(n+1)/2n=(n+1)2
所以楼主所问问题为:
(1+1)/2+(2+1)/2+(3+1)/2+……+(n+1)/2
=(1+2+3+……+n)/2+n*(1/2)
=(n(n+1)/2)/2+n/2
=n*(n+1)/4+n/2
=n*n+3n/4
(3)1/2+1/4+1/8+1/16+1/32+1/64
=(32+16+8+4+2+1)/64
=63/64
(4)1/1×2×3+1/2×3×4+1/3×4×5+……+1/98×99×100
=1/2[(1/1×2-1/2×3)+(1/2×3-1/3×4)+……(1/98×99-1/99×100)
=1/2(1-1/9900)
=9899/19800