Giải thích các bước giải:
\(\begin{array}{l}
S = 1 + q + {q^2} + {q^3} + {q^4} + .... + {q^n} = \frac{{{q^{n + 1}} - 1}}{{q - 1}}\,\,\,\,\left( {q \ne 1} \right)\\
a,\\
S = 1 + 2 + 4 + 8 + .... + {2^{63}}\\
= 1 + 2 + {2^2} + {2^3} + .... + {2^{63}}\\
= \frac{{{2^{64}} - 1}}{{2 - 1}}\\
= {2^{64}} - 1\\
b,\\
S = 1 + 10 + 100 + ..... + 1000000\\
= 1 + 10 + {10^2} + ..... + {10^6}\\
= \frac{{{{10}^7} - 1}}{{10 - 1}}\\
= \frac{{{{10}^7} - 1}}{9}\\
c,\\
S = 9 + 99 + 999 + ..... + 9999999\\
= \left( {10 - 1} \right) + \left( {{{10}^2} - 1} \right) + \left( {{{10}^3} - 1} \right) + ... + \left( {{{10}^7} - 1} \right)\\
= \left( {10 + {{10}^2} + {{10}^3} + ... + {{10}^7}} \right) - 7\\
= \left( {1 + 10 + {{10}^2} + {{10}^3} + .... + {{10}^7}} \right) - 7\\
= \frac{{{{10}^8} - 1}}{{10 - 1}} - 7\\
= \frac{{{{10}^8} - 1}}{9} - 7\\
= \frac{{{{10}^8} - 64}}{9}
\end{array}\)
