Question

bài 1:

a)A=4+4²+4³+........+4¹⁰⁰⁰

b) B=1-2+2²-2³+2⁴-2⁵+.........+2¹⁰⁰⁰

c) C=1-5+5²-5³+.....+5²⁰⁰

Answer 1

Yêu cầu của bài là gì vậy bạn ???

Answer 2

\(A=4+4^2+4^3+...+4^{100}\)

\(4A=4^2+4^3+...+4^{1001}\)

\(4A-A=\left(4^2+4^4+...+4^{1001}\right)-\left(4+4^2+...+4^{1000}\right)\)

\(3A=4^{1001}-4\)

\(A=\dfrac{4^{1001}-4}{3}\)

Answer 3

C = 1 - 5 + 5² - 5³ + ... + 5²⁰⁰

5C = 5 - 5² + 5³ + ... + 5²⁰¹

C + 5C= (1 - 5 + 5² - 5³ + ... + 5²⁰⁰ ) + ( 5 - 5² + 5³ + ... + 5²⁰¹)

6C = 1 + 5²⁰¹

C = \(\dfrac{1+5^{201}}{6}\)

Answer 4

B = \(1-2\) + \(2^2+2^3+...+2^{1000}\)

\(2B=2-2^2+2^3-...+2^{1001}\)

\(B+2B=\)(\(1-2\) \(+\)\(2^2+2^3+...+2^{1000}\)) +( \(2-2^2+2^3-...+2^{1001}\))

\(3B=1+2^{1001}\)

\(B=\dfrac{1+2^{1001}}{3}\)

Answer 5

a, \(A=4+4^2+4^3+...+4^{1000}\)

\(4A=4^2+4^3+4^4+...+4^{1001}\)

\(4A-A=\left(4^2+4^3+4^4+...+4^{1001}\right)-\left(4+4^2+4^3+...+4^{1000}\right)\)

\(3A=4^{1001}-\text{4}\Rightarrow A=\dfrac{4^{1001}-4}{3}\)

Answer 6

c, \(C=1-5+5^2-5^3+...+5^{200}\)

\(5C=5-5^2+5^3+...+5^{201}\)

\(6C=1+5^{201}\)

\(C=\dfrac{1+5^{201}}{6}\)