Question

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

Tính S ?

Answer 1

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

\(2S-S=2^{101}-2\)

\(S=\frac{2^{101}-2}{2}\)

Answer 2

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

\(2S=2.\left(2+2^2+2^3+2^4+...+2^{100}\right)\)

\(2S=2^2+2^3+2^4+2^5+...+2^{101}\)

\(2S-S=\left(2^2+2^3+2^4+2^5+...+2^{101}\right)-\left(2+2^2+2^3+2^4+...+2^{100}\right)\)

\(S=2^{101}-2\)