Question

Tính hợp lí:

a, A= \(\dfrac{1}{3}+\dfrac{1}{3^2}\)+\(\dfrac{1}{3^3}\)+....+\(\dfrac{1}{3^{2017}}\)+\(\dfrac{1}{3^{2018}}\)

b, B=1+5+\(5^2\)+\(5^3\)+....+\(5^{100}\)

c, C= \(2^{100}\) - \(2^{99}\) - \(2^{98}\) - \(2^{97}\) +....+ \(2^2\) - 2

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Answer 1

Answer 2

\(a,A=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{2017}}+\dfrac{1}{2^{2018}}\)

\(3A=1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{2016}}+\dfrac{1}{3^{2017}}\)

\(3A-A=1-\dfrac{1}{3^{2018}}\)

\(A=\dfrac{\left(1-\dfrac{1}{3^{2018}}\right)}{2}\)

\(b,B=1+5+5^2+5^3+...+5^{100}\)

\(5B=5+5^2+5^3+5^4+...+5^{100}+5^{101}\)

\(5B-B=1-5^{101}\)

\(B=\dfrac{\left(1-5^{101}\right)}{4}\)