Question

巧算下列各题

0.2+0.4+...+0.8+0.10+0.12+...+0.98+0.100
1/100+2/100+3/100+4/100+...+96/100+97/100+98/100+99/100

Answer 1

0.2+0.4+...+0.8+0.10+0.12+...+0.98+0.100
=(0.2+0.4+0.6+0.8) +(0.12+0.14+0.16+0.18)+..+(0.92+0.94+0.96+0.98)
+(0.1+0.2+..+0.9) +0.1
=2(0.2+0.8) + 2(0.12+0.18)+...+2(0.92+0.98) + (0.9+0.1)9/2 + 0.1
=2(1+0.3+0.5+..+1.9) + 9/2+0.1
=2( 1+ 9(0.3+1.9)/2) +9/2 +0.1
=2(1+ 9.9) +9/2 +0.1
=21.8+4.5+0.1
=26.4

1/100+2/100+3/100+4/100+...+96/100+97/100+98/100+99/100
= (1+2+..+99)/100
= [(1+99)99/2]/100
=99/2

Answer 2

等式1=（0.2+0.4+...+0.8）+（0.10+0.12+...+0.98）+0.100=2+24.3+0.1=26.4

等式2=(1/100+99/100)+(2/100+98/100)+(3/100+97/100)+(4/100+96/100)+......+(49/100+51/100)+50/100=49又1/2

Answer 3

0.2+0.4+...+0.8+0.10+0.12+...+0.98+0.100

=0.2×（1+2+3+4）+0.01×（10+12+……+98）+0.100
=0.2×10+0.01×（10+98）×45/2+0.100
=2+44.55+0.1
=46.65

1/100+2/100+3/100+4/100+...+96/100+97/100+98/100+99/100

=1/100×（1+2+3+4+……+98+99）
=1/100×（1+99）×99/2
=99/2
=49.5

Answer 4

第一道题没错的话就是26.4
第二道49.5
已经经过复算，正确

Answer 5

这个....你百度下等差数列就知道怎么巧算了