Cho S= 1+4+4^2+…+4^48+4^49 a) Tính S b) CMR : 4^50 : 3 dư 1 ????á???? ????ạ???? ℊ????ú???? ???????????? ????????????!

Question

Cho S= 1+4+4^2+…+4^48+4^49
a) Tính S
b) CMR : 4^50 : 3 dư 1
????á???? ????ạ???? ℊ????ú???? ???????????? ????????????!

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Ivy 2 tuần 2021-09-08T14:01:46+00:00 2 Answers 2 views 0

Answers ( )

    0
    2021-09-08T14:02:59+00:00

    a)S=1+4+4^2+…+4^48+4^49

     4S=4(1+4+4^2+…+4^48+4^49)

     4S=4+4^2+4^3+…+4^49+4^50

     4S-S=(4+4^2+4^3+…+4^49+4^50)-(1+4+4^2+…+4^48+4^49)

     3S=4^50-1

       S=$\frac{4^{50}-1}{3}$ 

    câu b thì mình ko nghĩ ra

    0
    2021-09-08T14:03:40+00:00

    Đáp án:

     

    Giải thích các bước giải:

    a)S=1+4+$4^2$+…+$4^{48}$+$4^{49}$

     4S=4(1+4+$4^2$+…+$4^{48}$+$4^{49}$)

     4S=4+$4^2$+$4^3$+…+$4^{49}$+$4^{50}$

     4S-S=(4+$4^2$+$4^3$+…+$4^{49}$+$4^{50}$)-(1+4+$4^2$+…+$4^{48}$+$4^{49}$)

    3S=$4^{50}$-1

    ⇒S=$\frac{4^{50}-1}{3}$

    Vây S=$\frac{4^{50}-1}{3}$

    b) Vì S=$\frac{4^{50}-1}{3}$  

    ⇒$4^{50}$-1⋮3

    ⇒$4^{50}$:3 dư 1

    Vậy $4^{50}$ :3 dư 1

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