Question

A=1+1/3+1/9+1/27+...+1/729x3

Answer 1

Ta có: \(A=1+\frac13+\frac19+\cdots+\frac{1}{729\times3}\)

=>\(A=1+\frac13+\frac19+\cdots+\frac{1}{2187}\)

=>\(3\times A=3+1+\frac13+\cdots+\frac{1}{729}\)

=>\(3\times A-A=3+1+\frac13+\cdots+\frac{1}{729}-1-\frac13-\cdots-\frac{1}{2187}\)

=>\(2\times A=3-\frac{1}{2187}=\frac{3\times2187-1}{2187}=\frac{6560}{2187}\)

=>\(A=\frac{6560}{2187}:2=\frac{3280}{2187}\)