Question

the sum of the following series 1/2 + 1/3^2 +1/2^3 + 1/ 3^4 + 1/2^5 + 1 / 3^6
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Answer 1

Answer:

(1/2+1/2^3+1/2^5)+(1/3^2+1/3^4+1/3^6)

=(1-1/4^3)/2(1-1/4)+1(1-1/9^3)/3(1-1/9)

=63/64×2/3+3/8×728/729

=21/32+91/243