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1/1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7+... = (1/1 + 1/2 + 1/4 +1/8+ ...) + (1/3 + 1/6 + 1/12 + 1/24 + 1/48 +... ) + (1/5 + 1/10 + 1/20 + 1/40 + 1/80 +...)+... ={(1/1 /(1-1/2) } + {(1/3/(1-1/2)} +{1/5/(1-1/2)}+... = 2(1/1) + 2(1/3) + 2(1/5)+... =2(1/1 + 1/3 + 1/5 + 1/7 + 1/9+...) So, 1/1+1/2+1/3+1/4+...=2(1/1+1/3+1/5+1/7+...) 1/2+1/4+1/6+1/8+...=1/1+1/3+1/5+1/7+... 1/2-1/3+1/4-1/5+1/6-1/7+1/8+...=1
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