Tính tổng của S S=2+2^2+2^3+2^4+…+2^100 S=2+2^3+2^5+…+2^99 S=3+3^3+3^4+…+3^50

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1. `S=2+2^2+2^3+2^4+…+2^100`
   `2S=2^2+2^3+2^4+2^5+…+2^101`
   `2S-S=(2^2+2^3+2^4+2^5+…+2^101)-(2+2^2+2^3+2^4+…+2^100)`
   `S=2^101-2`

   Vậy `S=2^101-2`

   `S=2+2^3+2^5+…+2^99`
   `2^2S=2^3+2^5+2^7+…+2^101`
   `4S-S=(2^3+2^5+2^7+…+2^101)-(2+2^3+2^5+…+2^99)`
   `3S=2^101-2`
   `S=[2^101-2]/3`
   Vậy `S=[2^101-2]/3`
   `S=3+3^2+3^3+3^4+…+3^50`
   `3S=3^2+3^3+3^4+3^5+…+3^51`
   `3S-S=(3^2+3^3+3^4+3^5+…+3^51)-(3+3^3+3^4+…+3^50)`
   `2S=3^51-3`
   `S=[3^51-3]/3`
   Vậy `S=[3^51-3]/3`

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2. Đáp án:

    

   Giải thích các bước giải:

   1)S=2+2²+2³+2^4+…+2^100

   ⇔2S=2²+2³+2^4+…+2^100+2^101

   ⇔2S-S= (2²+2³+2^4+…+2^100+2^101)-(2+2²+2³+2^4+…+2^100)

   ⇔S=2^101 – 2

   Vậy S=2^101-2

   2)S=2+2³+2^5+…+2^99

   ⇔2².S=2^3+2^5+2^7+..+2^101

   ⇔4.S-S=(2^3+2^5+2^7+..+2^101)-(2+2^3+2^5+..+2^99)

   ⇔3S=2^101 – 2

   ⇔S=(2^101 – 2):3

   Vậy S=(2^101-2):3

   3)S=3+3^3+3^4+…+3^50

   3S=S=3²+3^4+3^5+…+3^51

   3S-S=(3²+3^4+3^5+…+3^51) – (3+3^3+3^4+…+3^50)

   2S=3²+ 3^51 – 3 – 3³

   S=3^51

   Vậy S=3^51

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