JEE Main 2022 · 29 Jul · Shift 1 · Mathematics Q28

← JEE Main 2022 · 29 Jul · Shift 1

MathematicsInteger+4 / -1Question 28 of 90

If $\dfrac1{2\times3\times4}+\dfrac1{3\times4\times5}+\dfrac1{4\times5\times6}+\dots+\dfrac1{100\times101\times102}=\dfrac k{101}$ , then 34 k is equal to _______.

Your answer

Answer and worked solution

Official answer: 286

Telescope. $\dfrac1{n(n+1)(n+2)}=\dfrac12\left(\dfrac1{n(n+1)}-\dfrac1{(n+1)(n+2)}\right)$ , so the sum is $\dfrac12\left(\dfrac16-\dfrac1{101\cdot102}\right)=\dfrac{143}{17\cdot101}$ .

So $k=\frac{143}{17}$ and $34k=286$ .

Answer: 286

Topics:Special series sums

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JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 28