Câu hỏi của nanhdaynek

Question

Tính tống S=1+1/2+1/2^3+1/2^5+1/2^7+...+1/2^99+1/2^101

ILoveMath · Accepted Answer

$S=1+\dfrac{1}{2}+\dfrac{1}{2^3}+\dfrac{1}{2^5}+...+\dfrac{1}{2^{101}}$$\Rightarrow S-1=\dfrac{1}{2}+\dfrac{1}{2^3}+\dfrac{1}{2^5}+...+\dfrac{1}{2^{101}}$$\Rightarrow\dfrac{1}{4}\left(S-1\right)=\dfrac{1}{2^3}+\dfrac{1}{2^5}+\dfrac{1}{2^7}+...+\dfrac{1}{2^{103}}$$\Rightarrow\dfrac{1}{4}\left(S-1\right)-\left(S-1\right)=\dfrac{1}{2^3}+\dfrac{1}{2^5}+\dfrac{1}{2^7}+...+\dfrac{1}{2^{103}}-\dfrac{1}{2}-\dfrac{1}{2^3}-...-\dfrac{1}{2^{101}}$$\Rightarrow\dfrac{3}{4}\left(S-1\right)=\dfrac{1}{2^{103}}$$\Rightarrow S-1=\dfrac{1}{2^{103}}:\dfrac{3}{4}$$\Rightarrow S-1=\dfrac{4}{3.2^{103}}$$\Rightarrow S=\dfrac{4}{3.2^{103}}+1$Câu trả lời: $S=1+\dfrac{1}{2}+\dfrac{1}{2^3}+\dfrac{1}{2^5}+...+\dfrac{1}{2^{101}}$$\Rightarrow S-1=\dfrac{1}{2}+\dfrac{1}{2^3}+\dfrac{1}{2^5}+...+\dfrac{1}{2^{101}}$$\Rightarrow\dfrac{1}{4}\left(S-1\right)=\dfrac{1}{2^3}+\dfrac{1}{2^5}+\dfrac{1}{2^7}+...+\dfrac{1}{2^{103}}$$\Rightarrow\dfrac{1}{4}\left(S-1\right)-\left(S-1\right)=\dfrac{1}{2^3}+\dfrac{1}{2^5}+\dfrac{1}{2^7}+...+\dfrac{1}{2^{103}}-\dfrac{1}{2}-\dfrac{1}{2^3}-...-\dfrac{1}{2^{101}}$$\Rightarrow\dfrac{3}{4}\left(S-1\right)=\dfrac{1}{2^{103}}$$\Rightarrow S-1=\dfrac{1}{2^{103}}:\dfrac{3}{4}$$\Rightarrow S-1=\dfrac{4}{3.2^{103}}$$\Rightarrow S=\dfrac{4}{3.2^{103}}+1$

Đinh Đức Anh · Answer

S=1+12+123+125+...+12101S=1+12+123+125+...+12101⇒S−1=12+123+125+...+12101⇒S−1=12+123+125+...+12101⇒14(S−1)=123+125+127+...+12103⇒14(S−1)=123+125+127+...+12103⇒14(S−1)−(S−1)=123+125+127+...+12103−12−123−...−12101⇒14(S−1)−(S−1)=123+125+127+...+12103−12−123−...−12101⇒34(S−1)=12103⇒34(S−1)=12103⇒S−1=12103:34⇒S−1=12103:34⇒S−1=43.2103⇒S−1=43.2103⇒S=43.2103+1Câu trả lời: S=1+12+123+125+...+12101S=1+12+123+125+...+12101⇒S−1=12+123+125+...+12101⇒S−1=12+123+125+...+12101⇒14(S−1)=123+125+127+...+12103⇒14(S−1)=123+125+127+...+12103⇒14(S−1)−(S−1)=123+125+127+...+12103−12−123−...−12101⇒14(S−1)−(S−1)=123+125+127+...+12103−12−123−...−12101⇒34(S−1)=12103⇒34(S−1)=12103⇒S−1=12103:34⇒S−1=12103:34⇒S−1=43.2103⇒S−1=43.2103⇒S=43.2103+1

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