enEnglishhiहिन्दी
JEE Mains · Maths · STD 11 - 8. sequence and series
If \(n\) be odd or even, then the sum of \(n\) terms of the series \(1 - 2 + \) \(3 - \)\(4 + 5 - 6 + ......\) will be
- A \( - \frac{n}{2}\)
- B \(\frac{{n - 1}}{2}\)
- C \(\frac{{n + 1}}{2}\)
- D (a) and (c) both
Answer & Solution
Correct Answer
(D) (a) and (c) both
Step-by-step Solution
Detailed explanation
(d) Given series \(S = 1 - 2 + 3 - 4 + 5 - 6.........\) Case \(I\) : If \(n\) is odd, say \(2m + 1\) In this case, the number of positive terms \( = \frac{1}{2}(n + 1) = \frac{1}{2}(2m + 1 + 1) = (m + 1)\) and the number of negative terms \( = (2m + 1) - (m + 1) = m\) Then sum…
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
- A stair-case of length \(l\) rests against a vertical wall and a floor of a room. Let \(P\) be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio \(1 : 2\). If the staircase begins to slide on the floor, then the locus of \(P\) isJEE Mains 2014 Hard
- If for some \(\alpha \in R ,\) the lines \(L _{1}: \frac{ x +1}{2}=\frac{ y -2}{-1}=\frac{ z -1}{1}\) and \(L _{2}: \frac{ x +2}{\alpha}=\frac{ y +1}{5-\alpha}=\frac{ z +1}{1}\) are coplanar, then the line \(L _{2}\) passes through the pointJEE Mains 2020 Hard
- If the area of the region bounded by the curves, \(y = {x^2}\,,\,y = \frac{1}{x}\) and the lines \(y = 0\) and \(x = t (t > 1 )\) is \(1\,sq. unit\) , then \(t\) is equal toJEE Mains 2018 Hard
- The diameter of the circle, whose centre lies on the line \(x+y=2\) in the first quadrant and which touches both the lines \(x=3\) and \(y=2,\) isJEE Mains 2020 Hard
- If \(\left(\sin ^{-1} x\right)^{2}-\left(\cos ^{-1} x\right)^{2}=a ; 0\,<\,x\,<\,1, a \neq 0\), then the value of \(2 \mathrm{x}^{2}-1\) is :JEE Mains 2021 Hard
- Consider two sets \(A\) and \(B\), each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively and the sum and the product of the elements of B be 36 and q respectively. Let d and D be the common differences of AP's in A and B respectively such that \(D=d+3, d \gt 0\). If \(\frac{p+q}{p-q}=\frac{19}{5}\), then \(p-q\) is equal toJEE Mains 2025 Medium
More PYQs from JEE Mains
- Let \(A = \left\{ {0 \in \left( { - \frac{\pi }{2},\pi } \right):\frac{{3 + 2i\,\sin \,\theta }}{{1 - 2i\,\sin \,\theta }}\,{\rm{purely \,imaginary}}} \right\}\). Then the sum of the elements in \(A\) isJEE Mains 2019 Hard
- If \(z_1, z_2, z_3 \in C\) are the vertices of an equilateral triangle, whose centroid is \(\mathrm{z}_0\), then \(\sum_{\mathrm{k}=1}^3\left(\mathrm{z}_{\mathrm{k}}-\mathrm{z}_0\right)^2\) is equal toJEE Mains 2025 Medium
- If \(\frac{d y}{d x}=\frac{2^{x+y}-2^{x}}{2^{y}}, y(0)=1\), then \(y(1)\) is equal to :JEE Mains 2021 Hard
- The sum of all the four-digit numbers that can be formed using all the digits \(2,1,2,3\) is equal to \(.......\).JEE Mains 2023 Hard
- Consider the system of equations : \(x + ay = 0\), \(y + az = 0\) and \(z + ax = 0\). Then the set of all real values of \('a'\) for which the system has a unique solution isJEE Mains 2013 Hard
- Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a continuous function satisfying \(f(0)=1\) and \(f(2 \mathrm{x})-f(\mathrm{x})=\mathrm{x}\) for all \(\mathrm{x} \in \mathbb{R}\). If \(\lim _{n \rightarrow \infty}\left\{f(x)-f\left(\frac{x}{2^n}\right)\right\}=G(x)\), then \(\sum_{r=1}^{10} G\left(r^2\right)\) is equal toJEE Mains 2025 Hard