Đáp án+Giải thích các bước giải:

 `a)`

`100^{2}-99^{2}+98^{2}-97^{2}+...+2^{2}-1^{2}`

`=(100^{2}-99^{2})+(98^{2}-97^{2})+...+(2^{2}-1^{2})`

`=(100-99).(100+99)+(98-97).(98+97)+...+(2-1).(2+1)`

`=100+99+98+97+...+2+1`

`=(100+1).[(100-1):1+1]:2`

`=101.100:2`

`=101. 100. 1/2`

`=101. 50`

`=5050`

`b)`

`3.(2^{2}-1).(2^{4}+1)....(2^{64}+1)+1`

`=(2^{2}+1).(2^{2}-1).(2^{4}+1)....(2^{64}+1)+1`

`=(2^{4}-1).(2^{4}+1).(2^{8}+1)...(2^{64}+1)+1`

`=(2^{8}-1).(2^{8}+1).(2^{16}+1)...(2^{64}+1)+1`

`=(2^{16}-1).(2^{16}+1).(2^{32}+1).(2^{64}+1)+1`

`=(2^{32}-1).(2^{32}+1).(2^{64}+1)+1`

`=(2^{64}-1).(2^{64}+1)+1`

`=(2^{64})^{2}-1^{2}+1`

`=2^{128}-1+1`

`=2^{128}`