A = \(\dfrac{1}{4^2}\) + \(\dfrac{1}{4^3}\) + ...........+ \(\dfrac{1}{4^{100}}\)
A = \(\dfrac{1}{4^2}\) + \(\dfrac{1}{4^3}\)+...+ \(\dfrac{1}{4^{99}}\)+ \(\dfrac{1}{4^{100}}\)
4 \(\times\) A = \(\dfrac{1}{4}\) + \(\dfrac{1}{4^2}\) + \(\dfrac{1}{4^3}\) +...+ \(\dfrac{1}{4^{99}}\)
4A - A = \(\dfrac{1}{4}\) - \(\dfrac{1}{4^{100}}\)
3A = \(\dfrac{1}{4}\) - \(\dfrac{1}{4^{100}}\)
A = ( \(\dfrac{1}{4}\) - \(\dfrac{1}{4^{100}}\)): 3
A = \(\dfrac{1}{12}\) - \(\dfrac{1}{3\times4^{100}}\)
Đặt A=1/4^2 +...+1/4^100
4A=1/4+...+1/4^99
4A-A=(1/4+...+1/4^99)-(1/4^2+...+1/4^100)
3A=1/4-1/4^100
A=(1/4-1/4^100)/3
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