Đáp án:
Giải thích các bước giải:
`M = 1/2 + 1/2^2 + 1/2^3 +.............+ 1/2^100`
`2M = 1 + 1/2 + 1/2^2 +.............+ 1/2^99`
`2M - M = ( 1 + 1/2 + 1/2^2 +.............+ 1/2^99 ) - ( 1/2 + 1/2^2 + 1/2^3 +.............+ 1/2^100 )`
`M = 1 - 1/2^100`
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`N = 2^100 - 2^98 + 2^96 - 2^94 +..........+ 2^4 - 2^2`
`4N = 2^102 - 2^100 + 2^98 - 2^96 +.............+ 2^6 - 2^4`
`4N + N = ( 2^102 - 2^100 + 2^98 - 2^96 +.............+ 2^6 - 2^4 ) + ( 2^100 - 2^98 + 2^96 - 2^94 +..........+ 2^4 - 2^2 )`
`5N = 2^102 - 2^2`
`N = 2^102/5 - 4/5`
