Question

Tính A biết

A=1- \(\dfrac{1}{3}\)+\(\dfrac{1}{3^2}\)-\(\dfrac{1}{3^3}\)+...+\(\dfrac{1}{3^{102}}\)-\(\dfrac{1}{3^{103}}\)

Answer 1

\(3A=3-1+\dfrac{1}{3}-\dfrac{1}{3^2}+...+\dfrac{1}{3^{103}}-\dfrac{1}{3^{104}}\)

=>\(4A=3-\dfrac{1}{3^{104}}=\dfrac{3^{105}-1}{3^{104}}\)

=>\(A=\dfrac{3^{105}-1}{3^{104}\cdot4}\)

Answer 2

\(3A=3-1+\dfrac{1}{3}-\dfrac{1}{3^2}+...+\dfrac{1}{3^{103}}-\dfrac{1}{3^{104}}\)

=>\(4A=3-\dfrac{1}{3^{104}}=\dfrac{3^{105}-1}{3^{104}}\)

=>\(A=\dfrac{3^{105}-1}{3^{104}\cdot4}\)