Hãy luôn nhớ cảm ơn và vote 5*
nếu câu trả lời hữu ích nhé!
Tính tổng `S=1+3^3+3^5+3^7+...+3^103`
`3^2S=3^2.(1+3^3+3^5+3^7+...+3^103)`
`9S=3^2+3^5+3^7+3^9+...+3^105`
`9S-S=(3^2+3^5+3^7+3^9+...+3^105)-(1+3^3+3^5+3^7+...+3^103)`
`8S=3^105+3^2-3^3-1`
`8S=3^105+9-27-1`
`8S=3^105-19`
`S=(3^105-19)/8`
Vậy `S=(3^105-19)/8`
Tính tổng `S=1+1/2+1/2^3+1/2^5+1/2^7+...+1/2^99+1/2^101`
`S=1+1/2+1/2^3+1/2^5+1/2^7+...+1/2^99+1/2^101`
`2^2S=2^2.(1+1/2+1/2^3+1/2^5+1/2^7+...+1/2^99+1/2^101)`
`4S=4+2+1/2+1/2^3+1/2^5+1/2^7+...+1/2^97+1/2^99`
`4S-S=(4+2+1/2+1/2^3+1/2^5+1/2^7+...+1/2^97+1/2^99)-(1+1/2+1/2^3+1/2^5+1/2^7+...+1/2^99+1/2^101)`
`3S=4+2-1-1/2^101`
`3S=5-1/2^101`
`S=(5-1/2^101)/3`
Vậy `S=(5-1/2^101)/3`
Tính tổng `S=1+2+2^3+2^5+...2^99+2^101`
`S=1+2+2^3+2^5+...+2^99+2^101`
`2^2S=2^2.(1+2+2^3+2^5+...+2^99+2^101)`
`4S=4+2^3+2^5+2^7+...+2^101+2^103`
`4S-S=(4+2^3+2^5+2^7+...+2^101+2^103)-(1+2+2^3+2^5+...+2^99+2^101)`
`3S=2^103+4-1-2`
`3S=2^103+1`
`S=(2^103+1)/3`
Vậy `S=(2^103+1)/3`
Tính tổng `S=6^3+6^5+6^7+...+6^101`
`S=6^3+6^5+6^7+...+6^101`
`6^2S=6^2.(6^3+6^5+6^7+...+6^101)`
`36S=6^5+6^7+6^9+...+6^103`
`36S-S=(6^5+6^7+6^9+...+6^103)-(6^3+6^5+6^7+...+6^101)`
`35S=6^103-6^3`
`S=(6^103-6^3)/35`
Vậy `S=(6^103-6^3)/35`
Tính tổng `S=1/3+1/3^3+1/3^5+...+1/3^99+1/3^101`
`3^2S=3^2.(1/3+1/3^3+1/3^5+...+1/3^99+1/3^101)`
`9S=3+1/3+1/3^3+...+1/3^97+1/3^99`
`9S-S=(3+1/3+1/3^3+...+1/3^97+1/3^99)-(1/3+1/3^3+1/3^5+...+1/3^99+1/3^101)`
`8S=3-1/3^101`
`S=(3-1/3^101)/8`
Vậy `S=(3-1/3^101)/8`
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