Question

[Nguyễn Hoàng Bảo Hân]

D=1+4^2+4^4+4^6+...+4^100

Answer 1

[Nguyễn Minh Đăng]

Ta có: \(D=1+4^2+4^4+4^6+...+4^{100}\)

=> \(16D=4^2+4^4+4^6+4^8+...+4^{102}\)

=> \(16D-D=\left(4^2+4^4+...+4^{102}\right)-\left(1+4^2+...+4^{100}\right)\)

<=> \(15D=4^{102}-1\)

=> \(D=\frac{4^{102}-1}{15}\)

Answer 2

[FL.Han_]

\(D=1+4^2+4^4+4^6+...+4^{100}\)

\(16D=4^2+4^6+...4^{102}\)

\(16D-D=\left(4^2+4^6+...4^{102}\right)-\left(1+4^2+4^4+4^6+...+4^{100}\right)\)

\(15D=4^{102}-1\)

\(D=\frac{4^{102}-1}{15}\)