Question

Các bạn giúp mik nhanh lẹ với ạ!
Tính tổng: T=1+2^2+2^4+2^6+...+2^100
Anh nhanh mik tick lẹ liền.

Answer 1

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

\(\Rightarrow2^2\cdot T=2^2+2^4+2^6+2^8+....+2^{102}\)

\(\Rightarrow4T-T=\left(2^2+2^4+2^6+...+2^{102}\right)-\left(1+2^2+2^4+...+2^{100}\right)\)

\(\Rightarrow3T=2^{102}-1\Rightarrow T=\frac{2^{102}-1}{3}\)