Đáp án:
Giải thích các bước giải:
`a, A = 1 + 2 + 2^2 +...........+ 2^100`
`2A = 2 + 2^2 + 2^3 +..........+ 2^101`
`2A - A = ( 2 + 2^2 + 2^3 +..........+ 2^101 ) - ( 1 + 2 + 2^2 +...........+ 2^100 )`
`A = 2^101 - 1`
`b, B = 3^200 + 3^198 + 3^196 +.......+ 3^2 + 1`
`3^2B = 3^202 + 3^200 + 3^198 +.......+ 3^4 + 3^2`
`9B - B = ( 3^202 + 3^200 + 3^198 +.......+ 3^4 + 3^2 ) - ( 3^200 + 3^198 + 3^196 +.......+ 3^2 + 1 )`
`8B = 3^202 - 1`
`B = ( 3^202 - 1 )/8`
`c, C = 1/4 + 1/4^2 + 1/4^3 +...........+ 1/4^2021`
`1/4C = 1/4^2 + 1/4^3 + 1/4^4 +.........+ 1/4^2022`
`C - 1/4C = ( 1/4 + 1/4^2 + 1/4^3 +...........+ 1/4^2021 ) - ( 1/4^2 + 1/4^3 + 1/4^4 +.........+ 1/4^2022 )`
`3/4C = 1/4 - 1/4^2022`
`C = ( 1/4 - 1/4^2022 ) : 3/4`
`C = ( 1/4 - 1/4^2022 ) . 4/3`
`C = 1/3 - 1/( 4^2021 . 3 )`
`d, D = 1/5 + 1/5^3 + 1/5^5 +.........+ 1/5^2021`
`1/5^2D = 1/5^3 + 1/5^5 + 1/5^7 +........+ 1/5^2023`
`D - 1/5D = ( 1/5 + 1/5^3 + 1/5^5 +.........+ 1/5^2021 ) - ( 1/5^3 + 1/5^5 + 1/5^7 +........+ 1/5^2023 )`
`4/5D = 1/5 - 1/5^2023`
`D = 1/4 - 1/( 5^2022 . 4 )`
`e, E = 3^100 - 3^99 + 3^98 -.............- 3 + 1`
`3E = 3^101 - 3^100 + 3^99 -...........- 3^2 + 3`
`3E + E = ( 3^101 - 3^100 + 3^99 -...........- 3^2 + 3 ) + ( 3^100 - 3^99 + 3^98 -.............- 3 + 1 )`
`4E = 3^101 + 1`
`E = ( 3^101 + 1 )/4`
