Find the sum of the geometric series ∞Σ(n=1) [(−2)^(n−1)]/(5^n), or show that it is divergent.?

Sol
S=2^0/5^1－2^1/5^2+2^2/5^4－2^3/5^4+…...
－2S/5=2^1/5^2－2^2/5^3+2^3/5^4－………..
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3S/5=2^0/5^1
3S/5=1/5
S=1/3