1/1×4+1/4×7+1/7×10+...+1/22×25+1/25×28
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/25 06:56:28
1/1×4+1/4×7+1/7×10+...+1/22×25+1/25×28
![1/1×4+1/4×7+1/7×10+...+1/22×25+1/25×28](/uploads/image/z/18072513-9-3.jpg?t=1%2F1%C3%974%2B1%2F4%C3%977%2B1%2F7%C3%9710%2B...%2B1%2F22%C3%9725%2B1%2F25%C3%9728)
裂项:
1/(1×4)=1/3(1-1/4)
1/(4×7)=1/3(1/4-1/7)
.
1/(25×28)=1/3(1/25-1/28)
∴1/1×4+1/4×7+1/7×10+...+1/22×25+1/25×28
=1/3[(1-1/4)+(1/4-1/7)+(1/7-1/10)+.+(1/22-1/25)+(1/25-1/28)]
=1/3[1-1/28]
=9/28
1/(1×4)=1/3(1-1/4)
1/(4×7)=1/3(1/4-1/7)
.
1/(25×28)=1/3(1/25-1/28)
∴1/1×4+1/4×7+1/7×10+...+1/22×25+1/25×28
=1/3[(1-1/4)+(1/4-1/7)+(1/7-1/10)+.+(1/22-1/25)+(1/25-1/28)]
=1/3[1-1/28]
=9/28
计算:1×4×7+4×7×10+7×10×13+.+22×25×28
计算1×4+4×7+7×10+...+19×22+22×25
1*4+4*7+7*10+.+19*22+22*25怎么算
用简便方法计算: 1+4+7+10+13+16+19+22+25+28+31+34+37+40+4
1+4+7+10+13+16+19+22+25+28+31+34+37+40+43+46+49 用脱式计算
数列,1+4,7+10+13,16+19+22+25……第10项值是
1+2+3-4+5+6+7-8+9+10+11-12+.+25+26+27-28
11*10*9*8*7*6*5*4*3*2*1/(22*24*25*27)
有一串数字:1,4,7,10,13,16,19,22,25,、、、帮帮忙
1,4,7,10,13,16,19,22,25,...一百个数中的和是多少
(1/2-1/3)+(1/4-1/5)+(1/7-1/10)+(1/14-1/15)+(1/28-1/30)
(1/2-1/3)+(1/4-1/5)+(1/7-1/10)+(1/14-1/15)+(1/28-1/30))