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If the value oflim_(n to oo) n^(-n^2) ((n + 1)(n + 1/3)(n + 1/(3^2)) ….(n + 1/(3^(n-1))))^(n) is e^k then k is: |
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Answer» `=lim_(nrarroo)((n+1)/(n))^(n).((n+(1)/(3))/(n))^(n)"............"((n+(1)/(3^(n-1)))/(n))^(n)=lim_(nrarroo)(1+(1)/(n))^(n)(1+(1)/(3n))^((3n)/(3))"...."(1+(1)/(3^(n-1).n))^((3^(n-1).n)/(3^(n-1)))` `e.e^((1)/(3)).e^((1)/(9))"........"e^((1)/(3^(n-1)))=e^(1+(1)/(3)+(1)/(3^(2))"......."oo)=e^((1)/(1-1//3))=e^(3//2)","k=1.50` |
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