Question

S=1+2+2²+2³+.............+2⁸⁹

^{tinh tong}

Answer 1

\(S=1+2+2^2+.......+2^{89}\)

\(\Leftrightarrow2S=2+2^2+........+2^{90}\)

\(\Leftrightarrow2S-S=\left(2+2^2+........+2^{89}+2^{90}\right)-\left(1+2+........+2^{89}\right)\)

\(\Leftrightarrow S=2^{90}-1\)

Answer 2

S = 1 + 2 + 2² + 2³ + ......... + 2⁸⁹

S = 2⁰ + 2¹ + 2² + 2³ + ....... + 2⁸⁹

2¹ . S = 2¹ . ( 2⁰ + 2¹ + 2² + 2³ + ...... + 2⁸⁹ )

2S = 2¹ + 2² + 2³ + 2⁴ + .......... 2⁹⁰

2S - S = ( 2¹ + 2² + 2³ + 2⁴ + ....... + 2⁹⁰ ) - ( 1 + 2 + 2² + 2³ + ..... + 2⁸⁹ )

S = 2⁹⁰ - 1

Vậy S = 2⁹⁰ - 1