Question

Answer 1

`1`

`a)1/2+1/6+1/12+1/20+...+1/90`

`=1/1.2+1/2.3+1/3.4+1/4.5+...+1/9.10`

`=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10`

`=1-1/10`

`=9/10`

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`b)7/1.2+7/2.3+...+7/13.14`

`=7xx(1/1.2+1/2.3+1/3.4+...+1/13.14)`

`=7xx(1/1-1/2+1/2-1/3+1/3-1/4+...+1/13-1/14)`

`=7xx(1-1/14)`

`=7xx13/14`

`=91/14=13/2`

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`c)3/1.4+3/4.7+...+3/41.44`

`=1/1−1/4+1/4−1/7+1/7−1/10+...+1/41−1/44`

`=1−1/44`

`=43/44`