Tính a) A=4+ $2^{2}$ + $2^{3}$ + $2^{4}$ +….+ $2^{20}$ b) Tìm x biết: (x+1)+(x+2)+…+(x+100)=5750

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1. a, $A=4+2^2+2^3+…+2^{20}$

   $⇒2A=2^3+2^3+2^4+…+2^{21}$

   $⇒2A-A=(2+2)+2^{21}$

   $⇒A=2^{21}+4$

   b, $(x+1)+(x+2)+…+(x+100)=5750$

   $⇒100x+(1+2+…+100)=5750$

   $⇒100x+5050=5750$

   $⇒100x=700$

   $⇒x=7$

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2. Đáp án:

    

   Giải thích các bước giải: $$A=4+2^2+2^3+2^4+…+2^{20}\\2A=8+2^3+2^4+…+2^{21}\\\Leftrightarrow 2A-A=2^{21}+4=A=2097152$$

   b) $$(x+1)+(x+2)+…+(x+100)=5750\\\Leftrightarrow 100x+1+2+…+100=5750\\\Leftrightarrow 100x+\frac{100(100+1)}{2}=5750\\\Leftrightarrow 100x+5050=5750\\\Leftrightarrow 100x=700\\\Leftrightarrow x=7$$

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