Tính : a. 1+2+2 2 +2 3 +...+2 100 b. 1+3+3 2 +3 3 ...+3 100 Cần giúp làm gấp : </p...

a) Đặt \(A=1+2+2^2+2^3+...+2^{100}\) \(\Rightarrow2A=2+2^2+2^3+2^4+...+2^{101}\) \(\Rightarrow2A-A=A=\left(2+2^2+2^3+2^4+...+2^{101}\right)-\left(1+2+2^2+2^3+...+2^{100}\right)\) \(\Rightarrow A=2^{101}-1\) Vậy \(A=2^{101}-1\) b) Đặt \(B=1+3+3^2+3^3+...+3^{100}\) \(\Rightarrow3B=3+3^2+3^3+3^4+...+3^{101}\) \(\Rightarrow3B-B=2B=\left(3+3^2+3^3+3^4+...+3^{101}\right)-\left(1+3+3^2+3^3+...+3^{100}\right)\) \(\Rightarrow2B=3^{101}-1\) \(\Rightarrow B=\frac{3^{101}-1}{2}\) Vậy \(B=\frac{3^{101}-1}{2}\) _Chúc bạn học tốt_ Câu trả lời: a) Đặt \(A=1+2+2^2+2^3+...+2^{100}\) \(\Rightarrow2A=2+2^2+2^3+2^4+...+2^{101}\) \(\Rightarrow2A-A=A=\left(2+2^2+2^3+2^4+...+2^{101}\right)-\left(1+2+2^2+2^3+...+2^{100}\right)\) \(\Rightarrow A=2^{101}-1\) Vậy \(A=2^{101}-1\) b) Đặt \(B=1+3+3^2+3^3+...+3^{100}\) \(\Rightarrow3B=3+3^2+3^3+3^4+...+3^{101}\) \(\Rightarrow3B-B=2B=\left(3+3^2+3^3+3^4+...+3^{101}\right)-\left(1+3+3^2+3^3+...+3^{100}\right)\) \(\Rightarrow2B=3^{101}-1\) \(\Rightarrow B=\frac{3^{101}-1}{2}\) Vậy \(B=\frac{3^{101}-1}{2}\) _Chúc bạn học tốt_

Cảm ơn bạn nhé Nguyễn Thanh Hiền Câu trả lời: Cảm ơn bạn nhé Nguyễn Thanh Hiền

thanks bn nha Câu trả lời: thanks bn nha

Tính : a. 1+2+22+23+...+2100 b. 1+3+32+33....

Phan Nam Phong

9 tháng 7 2018 - olm

Tính :

a. 1+2+2²+2³+...+2¹⁰⁰

b. 1+3+3²+3³...+3¹⁰⁰

^{Cần giúp làm gấp :}

#Hỏi cộng đồng OLM #Toán lớp 6

Nguyễn Thanh Hiền

9 tháng 7 2018

a) Đặt \(A=1+2+2^2+2^3+...+2^{100}\)

\(\Rightarrow2A=2+2^2+2^3+2^4+...+2^{101}\)

\(\Rightarrow2A-A=A=\left(2+2^2+2^3+2^4+...+2^{101}\right)-\left(1+2+2^2+2^3+...+2^{100}\right)\)

\(\Rightarrow A=2^{101}-1\)

Vậy \(A=2^{101}-1\)

b) Đặt \(B=1+3+3^2+3^3+...+3^{100}\)

\(\Rightarrow3B=3+3^2+3^3+3^4+...+3^{101}\)

\(\Rightarrow3B-B=2B=\left(3+3^2+3^3+3^4+...+3^{101}\right)-\left(1+3+3^2+3^3+...+3^{100}\right)\)

\(\Rightarrow2B=3^{101}-1\)

\(\Rightarrow B=\frac{3^{101}-1}{2}\)

Vậy \(B=\frac{3^{101}-1}{2}\)

_Chúc bạn học tốt_

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Phan Nam Phong

9 tháng 7 2018

Cảm ơn bạn nhé Nguyễn Thanh Hiền

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Max Dieggo

11 tháng 10 2018

~~thanks bn nha~~

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Max Dieggo

11 tháng 10 2018

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Max Dieggo

11 tháng 10 2018

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