JEE Main 2014 · 12 Apr · Shift 1 · Mathematics Q69

MathematicsSingle correct+4 / -1Question 69 of 90

The least positive integer n such that $1-\dfrac23-\dfrac2{3^2}-\dots-\dfrac2{3^{n-1}}<\dfrac1{100}$ , is :

Answer and worked solution

Official answer: C

$1-2\left(\frac13+\dots+\frac1{3^{n-1}}\right)=1-\left(1-\frac1{3^{n-1}}\right)=\frac1{3^{n-1}}$ .

$3^{n-1}>100$ first holds at $n-1=5$ , so $n=6$ .

JEE Main 2014 · 12 Apr · Shift 1, Mathematics question 69