AP EAMCET · Maths · Sequences and Series
Let \(P(n): 1^2+2^2+3^2+\ldots+n^2\) \(=\frac{6(n-1)(n-2) \ldots(n-2020)+2 n^3+3 n^2+n}{6}\), for all \(n \in \mathbf{N}\). Then which of the following is correct?
- A \(P(n)\) is true for all \(n \in \mathrm{N}\)
- B \(P(n)\) is true for all \(h>2020\)
- C \(P(n)\) is true for all \(n \leq 2020\)
- D \(P(n)\) is not true for any \(n \in N\)
Answer & Solution
Correct Answer
(C) \(P(n)\) is true for all \(n \leq 2020\)
Step-by-step Solution
Detailed explanation
Given statement \(\begin{aligned} & P(n)=1^2+2^2+3^2+\ldots+n^2= \\ & \frac{6(n-1)(n-2) \ldots(n-2020)+2 n^3+3 n^2+n}{6} \end{aligned}\) \(\because\) We know that,…
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
- Let . ThenAP EAMCET 2021 Easy
- Let be such that and
Then the value of isAP EAMCET 2021 Medium - The quadratic equation whose roots are \(\sin ^2 18^{\circ}\) and \(\cos ^2 36^{\circ}\) is :AP EAMCET 2006 Medium
- If \(y=a \cos (\log x)+b \sin (\log x)\) then \(x^2 y_2+x y_1=\)AP EAMCET 2017 Medium
- \[
\begin{aligned}
& \text { If the } \\
& a x^2+2 h x y+b y^2+2 g x+2 f y+c=0
\end{aligned} \text { equation }
\]
represents a pair of straight lines, then the square of the distance of their point of intersection from the origin isAP EAMCET 2013 Medium - In a book of 250 pages, there are 200 typographical errors. Assuming that the number of errors per page follow the Poisson law, then the probability that a random sample of 5 pages will contain no typographical error isAP EAMCET 2019 Medium
More PYQs from AP EAMCET
- If the angle between the asymptotes of the hyperbola \(x^2-k y^2=3\) is \(\frac{\pi}{3}\) and \(e\) is its eccentricity, then the pole of the line \(x+y-1=0\) with respect to this hyperbola isAP EAMCET 2024 Medium
- If \(S_n=\int_0^{\frac{\pi}{2}} \frac{\sin (2 n-1) x}{\sin x} d x\) and \(n\) is an integer, then \(\mathrm{S}_{\mathrm{n}+1}-\mathrm{S}_{\mathrm{n}}=\)AP EAMCET 2023 Easy
- Maximum area of the rectangle inscribed in a circle of radius \(10 \mathrm{cms}\) isAP EAMCET 2022 Medium
- Which one of the following conditions is incorrect for a well behaved wave function \((\psi)\) ?AP EAMCET 2010 Easy
- 7 coins are tossed simultaneously and the number of heads turned up is denoted by the random variable X . If \(\mu\) is the mean and \(\sigma^2\) is the variance of \(X\), then \(\frac{\mu \sigma^2}{P(X=3)}=\)AP EAMCET 2024 Easy
- The descending order of magnitude of the eccentricities of the following hyperbolas is
A. A hyperbola whose distance between foci is three times the distance between its directrices.
B. Hyperbola in which the transverse axis is twice the conjugate axis.
C. Hyperbola with asymptotes
\(x+y+1=0, x-y+3=0\)AP EAMCET 2024 Easy