a) 1 + 2 + $2^{2}$ + $2^{3}$ +...+ $2^{100}$
Đặt A = 1 + 2 + $2^{2}$ + $2^{3}$ +...+ $2^{100}$
2A = 2 + $2^{2}$ + $2^{3}$ + $2^{4}$ ...+ $2^{101}$
2A - A = (2 + $2^{2}$ + $2^{3}$ + $2^{4}$ ...+ $2^{101}$) - (1 + 2 + $2^{2}$ + $2^{3}$ +...+ $2^{100}$)
A = $2^{101}$ - 1
b) 1 + a + $a^{2}$ + $a^{3}$ +...+ $a^{n}$
Đặt B = 1 + a + $a^{2}$ + $a^{3}$ +...+ $a^{n}$
2B = a + $a^{2}$ + $a^{3}$ + $a^{4}$ + ...+ $a^{n+1}$
2B - B = (a + $a^{2}$ + $a^{3}$ + $a^{4}$ + ...+ $a^{n+1}$) - (1 + a + $a^{2}$ + $a^{3}$ +...+ $a^{n}$)
B = $a^{n+1}$ - 1
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Xin hay nhất ạ!!~
