Question

数学题目，帮忙解答一下！

第一题：1\2 + 1\6 + 1\12 + 1\20 + 1\30 + 1\42
第二题：1\6 + 1\12 + 1\20 + 1\30 +…1\9900

Answer 1

1\2 + 1\6 + 1\12 + 1\20 + 1\30 + 1\42
=1-1\2+1\2-1\3+1\3-1\4+1\4-1\5+1\5-1\6+1\6-1\7
=6\7
1\6 + 1\12 + 1\20 + 1\30 +…1\9900
=1\2-1\3+1\3-1\4+1\4-1\5+1\5-1\6+...+1\99-1\100
=1\2-1\100
=49\100

Answer 2

谁那么聪明啊?

Answer 3

1 =(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/6-1/7)
=1-1/7=6/7
2 =1/2-1/3+1/3-1/4+...+1/99-1/100
=1/2-1/100=49/100

Answer 4

1.
1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42
=1/(1*2) +1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)
=[(1/1)-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+(1/4)-(1/5)+(1/5)-(1/6)+(1/6)-(1/7)]
=1-(1/7)
6/7;

2.
1/6 + 1/12 + 1/20 + 1/30 +…1/9900
=1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+...+1/(99*100)
=[(1/2)-(1/3)+(1/3)-(1/4)+(1/4)-(1/5)+...+(1/99)-(1/100)]
=(1/2)-(1/100)
=49/100.

Answer 5

1. =21/42+7/42+3.5/42+2.1/42+1.4/42
=35/42
=5/6

2. =1/2*3+1/3*4+1/4*5+...+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100
=1-1/100
=99/100

Answer 6

1. 6/7
2.49/100