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Evaluate Lt_(n to oo)[(1)/(1+n)+(1)/(2+n)+(1)/(3+n)+"...."+(1)/(10n)] |
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Answer» Solution :`underset(nrarr0)(LT)[(1)/(1+n)+(1)/(2+n)+(1)/(3+n)+"......"+(1)/(10N)] = underset(nrarroo)("Lt")underset(r=1)overset(9n)sum(1)/(r+n)` `=underset(nrarroo)(Lt)underset(r=1)overset(9n)sum(1)/(n) (1)/((r/n)+1) = underset(0)overset(9)int(dx)/(x+1)=[ln(x+1)]_(0)^(9)=ln10` |
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