Giúp em vs ạ:<< a)S=1+2+2^3+2^5+...+2^101 b)B=1+4+4^2+4^3+...4^1000 c)1+1/2+1/2^2+1/2^4+1/2^6+...+1/2^100

`#Rùa`

Đáp án:

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Giải thích các bước giải:

 `a) S=1+2+2^3+2^5+.....+2^{101}`

`->2^2S=2^2+2^3+2^5+2^7+.....+2^{103}`

`-> 2^2 S-S=(2^2+2^3+2^5+2^7+.....+2^{103})-(1+2+2^3+2^5+.....+2^{101})`

`-> 3S=2^2+2^{103}-3`

`-> 3S=2^{103}+1`

`-> S=(2^{103}+1)/3`

`b) B=1+4+4^2+4^3+...+4^{1000}`

`->4B=4+4^2+4^3+....+4^{1001}`

`-> 4B-B=(4+4^2+4^3+....+4^{1001})-(1+4+4^2+4^3+...+4^{1000})`

`-> 3B=4^{1001}-1`

`-> B=(4^{1001}-1)/3`

`c)C=1+1/2+1/2^2+1/2^4+1/2^6+...+1/2^{100}`

`->1/2^2 C=1/2^2+1/2^3+1/2^4+1/2^6+1/2^8+...+1/2^{102}`

`-> C-1/2^2 C =(1+1/2+1/2^2+1/2^4+1/2^6+...+1/2^{100})-(1/2^2+1/2^3+1/2^4+1/2^6+1/2^8+...+1/2^{102})`

`-> 3/4C=1+1/2-1/2^3-1/2^{102}`

`-> 3/4C=3/2-1/2^3-1/2^{102}`

`-> C=(3/2-1/2^3-1/2^{102})*4/3`

`-> C=2-1/2-1/2^{100}`

`-> C=3/2-1/2^{100}`