Question

Answer 1

`a, 81F = 9^2 + 9^4 + .. .+ 9^102`

`81F - F = (9^2 + 9^4 + ... + 9^102) - (1 +9^2+...+9^100)`

`80F = 9^102 - 1`

`F = (9^102-1)/80`

`b, 4G= 2^2 + 2^4 + ... + 2^102`

`4G - G = (2^2+2^4+ .. +2^102) - (1 + 2^2+...+2^100)`

`3G = 2^102-1`

`G = (2^102-1)/3`

`c, 9H = 3^2 + 3^4 + ... + 3^102`

`9H - H = (3^2 +3^4 + ... + 3^102) - (1 + 3^2 + ... + 3^100)`

`8H = 3^102 - 1`

`H = (3^102-1)/8`

`d, M = 1 + 2^3 + 2^6 + ... + 2^120`

`8M = 2^3 +2^6 + ... + 2^123`

`8M - M = (2^3+...+2^123) - (1 + 2^3 + .. + 2^120)`

`7M = 2^123 - 1`

`M = (2^123-1)/7`