`a)`
` A = 1 + 2 + 2^2 + ............. + 2^100`
`2A = 2 + 2^2 + ................... + 2^101`
` 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`
`8B = 3^202 - 1`
` B = (3^202 - 1)/8`
`c)`
` C = 1/4 + 1/(4^2) + 1/(4^3) + ............... + 1/(4^2021)`
`4C = 1 + 1/4 + 1/(4^2) + ................. + 1/(4^2020)`
`3C = 1 - 1/(4^2021)`
` C = (1 - 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)^2023`
`24/25D = 1/5 - (1/5)^2023`
` D = (1/5 - (1/5)^2023) : 24/25`
`e)`
` E = 3^100- 3^99+ 3^98 - 3^97 + ..............+ 3^2 - 3 + 3^0`
`3E = 3^101 - 3^100 + 3^99 - 3^98 + ............. + 3^3 - 3^2 + 3^1`
`4E = 3^101 + 1`
` E = (3^101 + 1)/4`
