Câu `1`

`(1 + 1/51) xx (1+1/52) xx (1+1/53) xx ... xx (1+1/1963)`

`= 52/51 xx 53/52 xx 54/53 xx ... xx 1964/1963`

`= (52xx53xx54xx...xx1964)/(51xx52xx53xx...xx1963)`

`= 1964/51`

Câu `2`

`(1-1/400) xx (1-1/401) xx (1-1/402) xx ... xx (1-1/2022)`

`= 399/400 xx 400/401 xx 401/402 xx ... xx 2021/2022`

`= (399xx400xx401 xx ... xx 2021)/(400 xx 401 xx 402 xx ... xx 2022)`

`= 399/2022`

Câu `3`

`1/(2xx4) + 1/(4xx7) + 1/(7xx10) + ... + 1/(37xx40)`

`= 1/8 + 1/3 xx (3/(4xx7) + 3/(7xx10) + ... + 3/(37xx40))`

`= 1/8 + 1/3 xx (1/4 - 1/7 + 1/7 - 1/10 + ... + 1/37 - 1/40)`

`= 1/8 + 1/3 xx (1/4 - 1/40)`

`= 1/8 + 1/3 xx 9/40`

`= 1/8 + 9/120`

`=1/5`

`#dtkc`

`#phuc`
`1`.
`( 1 + 1/51 ) xx ( 1 + 1/52 ) xx ( 1 + 1/53 ) xx ...... xx ( 1 + 1/1963 )`
` = 52/51 xx 53/52 xx 54/53 xx ...... xx 1964/1963`
` = { 52 xx 53 xx 54 xx .... xx 1964 }/{ 51 xx 52 xx 53 xx .... xx  1963 }`
` = 1964/51`

`2`.
`( 1 - 1/400 ) xx ( 1 - 1/401 ) xx ( 1 - 1/402 ) xx .... xx ( 1 - 1/2022 )`
` = 399/400 xx 400/401 xx 401/402 xx .... xx 2021/2022`
` = { 399 xx 400 xx 401 xx .... xx 2021 }/{ 400 xx 401 xx 402 xx .... xx 2022 }`
` = 399/2022`

`3`.
`1/{2 xx 4} + 1/{4 xx 7} + 1/{7 xx 10} + .... + 1/{37 xx 40}`
` = 1/8 + 1/3 xx ( 3/{4 xx 7} + 3/{7 xx 10} + ... + 3/{37 xx 40}`
` = 1/8 + 1/3 xx ( 1/4 - 1/7 + 1/7 - 1/10 + 1/10 + .... + 1/37 - 1/40 )`
` = 1/8 + 1/3 xx 9/40`
` = 1/8 + 3/40`
` = 5/40 + 3/40`
` = 8/40`
` = 1/5`