Question

[phạm minh vũ]

A= 2+2^2+2^3+...+2^19+2^20

b=2+2^3+2^5+...2^97+2^99

C=5+5^2+5^3+...+5^50

D=1+3+3^2+3^3+...+3^100

Answer 1

[Minh Hiếu]

\(2A-A=\left(2^2+2^3+...+2^{21}\right)-\left(2+2^2+...+2^{20}\right)\)

\(A=2^{21}-2\)

B tương tự câu A

\(5C-C=\left(5^2+5^3+...+5^{51}\right)-\left(5+5^2+...+5^{50}\right)\)

\(C=\dfrac{5^{51}-5}{4}\)

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

\(D=\dfrac{3^{101}-1}{2}\)

Answer 2

[Nguyễn Đăng Nhân]

\(A=2^1+2^2+2^3+...+2^{20}\)

\(2\cdot A=2^2+2^3+2^4+...+2^{21}\)

\(A=2^{21}-2\)

\(B=2^1+2^3+2^5+...+2^{99}\)

\(4\cdot B=2^3+2^5+2^7+...+2^{101}\)

\(B=\)\(\left(2^{101}-2\right):3\)

\(C=5^1+5^2+5^3+...+5^{50}\)

\(5\cdot C=5^2+5^3+5^4+...+5^{51}\)

\(C=(5^{51}-5):4\)

\(D=3^0+3^1+3^2+...+3^{100}\)

\(3\cdot D=3^1+3^2+3^3+...+3^{101}\)

\(D=(3^{101}-1):2\)