найти сумму последовательности 1/2-1/3+1/4-1/9+1/8-1/27+1/16-1/81 и т.д. Created by 777NEO777. algebra-ru

81 и т.д...

777NEO777 @777NEO777

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найти сумму последовательности 1/2-1/3+1/4-1/9+1/8-1/27+1/16-1/81 и т.д

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au456

Verified answer

S= (1/2+1/4+1/8+...)-(1/3+1/9+1/27+...)=S1-S2
S1=1/2+1/2*(1/2+1/4+1/8+...)=1/2+1/2S1
S1=1
S2=1/3+1/3*(1/3+1/9+1/27+...)=1/3+1/3S2
S2=1/2
S=S1-S2=1-1/2=1/2

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