TS EAMCET · Maths · Sequences and Series
For all , if , then
- A
- B
- C
- D
Answer & Solution
Correct Answer
(A)
Step-by-step Solution
Detailed explanation
We have, 12+22+32+…+n2>x ⇒nn+12n+16>x ⇒2n3+3n2+n6>x =n33+n22+n6>x So, the above expression always greater than n33. ∴ x=n33
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(x\) is so small that all terms containing \(x^2\) and higher powers of \(x\) can be neglected, then the approximate value of \(\frac{\left(1+\frac{2 x}{3}\right)^{-4}(4+5 x)^{1 / 2}}{(9+x)^{3 / 2}}\) when \(x=\frac{6}{371}\), isTS EAMCET 2020 Medium
- To remove the second term of the equation \(x^4-8 x^3+x^2-x+3=0\), diminish the roots of the equation byTS EAMCET 2002 Medium
- The number of roots of the equation \(\sqrt{2}+e^{\cosh ^1 x}-e^{\sinh { }^1 x}=0\), isTS EAMCET 2019 Medium
- If \(\omega\) is a complex cube root of unity, then \(\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}\) is equal toTS EAMCET 2008 Medium
- If the function defined by is right continuous at thenTS EAMCET 2019 Easy
- unbiased coins are tossed. The probability of having the number of heads is not equal to the number of tails isTS EAMCET 2020 Medium
More PYQs from TS EAMCET
- The general solution of the differential equation \(\frac{d y}{d x}+\frac{y}{x}=x^2\) isTS EAMCET 2023 Easy
- In a \(\triangle A B C\), if the medians \(A D\) and \(B E\) are such that \(A D=4, \angle D A B=\frac{\pi}{6}\) and \(\angle A B E=\frac{\pi}{3}\) then the area of \(\triangle A B C\) (in square units) isTS EAMCET 2019 Medium
- Two bodies were thrown simultaneously from the origin: one straight up and the other, at an angle, to the vertical. The initial velocity of each body is equal to Neglecting the air resistance, the distance between the two bodies after is ()TS EAMCET 2021 Easy
- A small object slides down with initial velocity equal to zero from the top of a smooth hill of height . The other end of the hill is horizontal and is at height as shown in the figure. The horizontal distance covered by the object from the end of the hill to the ground is
TS EAMCET 2022 Easy - Consider the following statements
Assertion (A): For \(x \in \mathbb{R}-\{1\}, \frac{d}{d x}\left(\operatorname{Tan}^{-1}\left(\frac{1+x}{1-x}\right)\right)=\frac{d}{d x}\left(\operatorname{Tan}^{-1} x\right)\)
Reason (R): For \(x < 1, \operatorname{Tan}^{-1}\left(\frac{1+x}{1-x}\right)=\frac{\pi}{4}+\operatorname{Tan}^{-1} x\),
for \(x>1, \operatorname{Tan}^{-1}\left(\frac{1+x}{1-x}\right)=-\frac{3 \pi}{4}+\operatorname{Tan}^{-1} x\)
The correct answer isTS EAMCET 2025 Medium - If \(x=\sec h^{-1} \frac{1}{2}+\tan h^{-1} \frac{1}{2}\), then \(\cos h x=\)TS EAMCET 2020 Hard