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a+ar+ar^(2)+...+ar^(n-1)=(a(1-r^(n)))/(1...

`a+ar+ar^(2)+...+ar^(n-1)=(a(1-r^(n)))/(1-r) forall n in N.`

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Statement -1 For all natural numbers n , 0.5+0.55+0.555+...... upto n terms =(5)/(9){n-(1)/(9)(1-(1)/(10^n))} , Statement-2 a+ar+ar^2+....+ar^(n-1)=(a(1-r^n))/((1-r)) , for 0lt r lt 1 .

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