TS EAMCET · Maths · Sequences and Series
For any integer \(n \geq 1, \sum_{K=1}^n K(K+2)=\)
- A \(\frac{n(n+1)(n+2)}{6}\)
- B \(\frac{n(n+1)(2 n+7)}{6}\)
- C \(\frac{n(n+1)(2 n+1)}{6}\)
- D \(\frac{n(n-1)(2 n+8)}{6}\)
Answer & Solution
Correct Answer
(B) \(\frac{n(n+1)(2 n+7)}{6}\)
Step-by-step Solution
Detailed explanation
Consider,…
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
- The number of complex roots of the equation \(x^{11}-x^7+x^4-1=0\) whose arguments lie in the first quadrant isTS EAMCET 2018 Easy
- If the line \(y=-4 x+b\) is tangent to the curve \(y=\frac{1}{x}\), then \(b\) equalsTS EAMCET 2015 Easy
- Consider the vectors and If and are length of projections of on on and on respectively, thenTS EAMCET 2021 Easy
- Let \(\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and \(\mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\). If \(\mathbf{c}\) is \(\mathbf{a}\) unit vector such that \(\left[\begin{array}{lll}\mathbf{a} & \mathbf{b} & \mathbf{c}\end{array}\right]\) is maximum, then \(\mathbf{c}=\)TS EAMCET 2020 Easy
- If \(z=1+i \sqrt{3}\) then \(|\operatorname{Arg} z|+|\operatorname{Arg} \bar{z}|\) is equal toTS EAMCET 2010 Hard
- If is the image of the point with respect to the straight line , then the length of the perpendicular drawn from to the line isTS EAMCET 2022 Easy
More PYQs from TS EAMCET
- If a function \(f\) is defined by \(f(x)=\frac{\cot ^3 x-\tan x}{\cos (x+\pi / 4)}(x \neq \pi / 4)\), then \(\lim _{x \rightarrow \frac{\pi}{4}} f(x)=\)TS EAMCET 2023 Easy
- A man can swim with a speed of \(4 \mathrm{kmh}^{-1}\) in still water. How long does he take to cross a river \(1 \mathrm{~km}\) wide, if the river flows steadily \(3 \mathrm{kmh}^{-1}\) and he makes his strokes normal to the river current?TS EAMCET 2021 Easy
- The differential equation of the family of circles with fixed radius units and centre on the line , isTS EAMCET 2022 Medium
- If \(\frac{x-4}{x^2-5 x+6}\) can be expanded in the ascending powers of \(x\), then the coefficient of \(x^3\) isTS EAMCET 2004 Medium
- If \(\int \frac{x^{49} \tan ^{-1}\left(x^{50}\right)}{\left(1+x^{100}\right)} d x=k\left(\tan ^{-1}\left(x^{50}\right)\right)^2+c\), then \(k=\)TS EAMCET 2023 Medium
- A source of sound of frequency \(640 \mathrm{~Hz}\) is moving at a velocity of \(\frac{100}{3} \mathrm{~m} / \mathrm{s}\) along a road, and is at an instant \(30 \mathrm{~m}\) away from a point \(A\) on the road (as shown in figure). A person standing at \(O, 40 \mathrm{~m}\) away from the road hears sound of apparent frequency \(v^{\prime}\). The value of \(v^{\prime}\) is (velocity of sound \(=340 \mathrm{~m} / \mathrm{s}\) )
TS EAMCET 2013 Hard