Đáp án:
`g)5` `050`
`h)2^128`
Giải thích các bước giải:
`g)100²-99²+98²-97²+...+2²-1²`
`=(100²-99²)+(98²-97²)+...+(2²-1²)`
`=(100+99)(100-99)+(98+97)(98-97)+...+(2+1)(2-1)`
`=(100+99).1+(98+97).1+...+(2+1).1`
`=100+99+98+97+...+2+1`
`text{-Số số hạng:(100-1):1+1=100(số hạng)}`
`text{-Tổng:(100+1).100:2=5 050}`
`h)3(2²+1)(2^4+1)(2^8+1)...(2^64+1)+1`
`=(2²-1)(2²+1)(2^4+1)(2^8+1)...(2^64+1)+1`
`=[(2^2)^2-1](2^4+1)(2^8+1)...(2^64+1)+1`
`=(2^4-1)(2^4+1)(2^8+1)...(2^64+1)+1`
`=[(2^4)^2-1^2](2^8+1)...(2^64+1)+1`
`=(2^8-1)(2^8+1)...(2^64+1)+1`
`=[(2^8)^2-1^2]...(2^64+1)+1`
`=(2^16-1)...(2^64+1)+1`
`=(2^64)^2-1^2+1`
`=2^128-1+1`
`=2^128`
