Question

Rút gọn 

A=1+2+2²+2³+.......+2¹⁰⁰

B=5+5²+5³+.........+5²⁰¹⁶

Answer 1

nhân 2A lên, nhân 5B lên rồi tự làm

Answer 2

Lm A ví dụ trước nha :

\(A=1+2+2^2+2^3+....+2^{100}\)

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

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

Answer 3

\(A=1+2+2^2+...+2^{100}\)

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

\(\Rightarrow2A-A=2^{101}-1\)

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

\(B=5+5^2+5^3+...+5^{2016}\)

\(\Rightarrow5B=5^2+5^3+5^4+...+5^{2017}\)

\(\Rightarrow5B-B=5^{2017}-5\)

\(\Rightarrow4B=5^{2017}-5\)

\(\Rightarrow B=\frac{5^{2017}-5}{4}\)

Answer 4

2a=2+2^2+2^3+...+2^101

2a-a=(2+2^2+2^3+...+2^101)-(1+2+2^2+2^3+...+2^100)

a=101-1

a=100

Bài B tương tự

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