JEE Main 2022 · 25 Jun · Shift 1 · Mathematics Q30

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MathematicsInteger+4 / -1Question 30 of 90

The greatest integer less than or equal to the sum of first 100 terms of the sequence $\dfrac13,\dfrac59,\dfrac{19}{27},\dfrac{65}{81},\dots$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 98

General term. $\dfrac{3^n-2^n}{3^n}=1-\left(\dfrac23\right)^n$ .

Sum. $100-2\left(1-\left(\frac23\right)^{100}\right)=98+2\left(\frac23\right)^{100}$ , just above 98.

Answer: 98

Topics:Geometric progression

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JEE Main 2022 · 25 Jun · Shift 1, Mathematics question 30