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Find the value of {:(""SigmaSigma),(1 le i le j):}" "i xx (1/2)^j |
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Answer» `=1xx[(1/2)^(2)+(1/2)^(3)+(1/2)^(4)+…]` `+2xx[(1/2)^(3)+(1/2)^(4)+(1/2)^(5)+..]` `+3xx[(1/2)^(4)+(1/2)^(5)+(1/2)^(6)+…]` ….. `=1xx((1/2)^(2))/(1-(1/2))+2xx((1/2)^(3))/(1-(1/2))+3xx((1/2)^(4))/(1-(1/2))+..` `thereforeS=1xx(1/2)+2xx(1/2)^(2)+3xx(1/2)^(3)+...` `therefore (1/2)S=1xx(1/2)^(2)+2xx(1/2)^(3)+3xx(1/2)^(4)...` Subtracting, we GET `(1/2)S=(1/2)+(1/2)^(2)+(1/2)^(3)+(1/2)^(4)+...=(1/2)/(1-1/2)=1` `therefore` S=2 |
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