JEE Mains · Maths · STD 11 - 8. sequence and series
The sum of first \(9\) terms of the series \(\frac{{{1^3}}}{1} + \frac{{{1^3} + {2^3}}}{{1 + 3}} + \frac{{{1^3} + {2^3} + {3^3}}}{{1 + 3 + 5}} + .\;.\;.\;.\)
- A \(192\)
- B \(71\)
- C \(96\)
- D \(142\)
Answer & Solution
Correct Answer
(C) \(96\)
Step-by-step Solution
Detailed explanation
Central idea Write the nth term of the given series and simplify it to get its lowest form. Then, apply, \(S_{n}=\Sigma T_{n}.\) Given series is \(\frac{{{1^3}}}{1} + \frac{{{1^3} + {2^3}}}{{1 + 3}} + \frac{{{1^3} + {2^3} + {3^3}}}{{1 + 3 + 5}} + \ldots \infty \) Let \(T_{n}\)…
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 \(\mathrm{f}: \mathbf{R} \rightarrow \mathbf{R}\) be a twice differentiable function such that \(f(2)=1\). If \(\mathrm{F}(x)=x f(x)\) for all \(x \in \mathbf{R}\), \(\int_0^2 x \mathrm{~F}^{\prime}(x) \mathrm{d} x=6\) and \(\int_0^2 x^2 \mathrm{~F}^{\prime \prime}(x) \mathrm{d} x=40\), then \(\mathrm{F}^{\prime}(2)+\int_0^2 \mathrm{~F}(x) \mathrm{d} x\) is equal to :JEE Mains 2025 Medium
- Let the area of the triangle formed by the lines \(x+2=y-1=z, \frac{x-3}{5}=\frac{y}{-1}=\frac{z-1}{1}\) and \(\frac{x}{-3}=\frac{y-3}{3}=\frac{z-2}{1}\) be \(A\). Then \(A^2\) is equal to ________JEE Mains 2025 Medium
- Let the positive integers be written in the form :
If the \(\mathrm{k}^{\text {th }}\) row contains exactly \(\mathrm{k}\) numbers for every natural number \(\mathrm{k}\), then the row in which the number \(5310\) will be, is .........JEE Mains 2024 Hard - When a certain biased die is rolled, a particular face occurs with probability \(\frac{1}{6}-\mathrm{x}\) and its opposite face occurs with probability \(\frac{1}{6}+\mathrm{x}\). All other faces occur with probability \(\frac{1}{6}\). Note that opposite faces sum to \(7\) in any die. If \(0\,<\,x\,<\,\frac{1}{6}\), and the probability of obtaining total \(\mathrm{sum}=7\), when such a die is rolled twice, is \(\frac{13}{96}\), then the value of \(x\) is:JEE Mains 2021 Hard
- The number of points in the interval \([2, 4]\), at which the function \(f(x) = \left[x^2 - x - \dfrac{1}{2}\right]\), where \([\cdot]\) denotes the greatest integer function, is discontinuous, is _______.JEE Mains 2026 Hard
- Let \(z _{1}\) and \(z _{2}\) be two complex numbers such that \(\overline{ z }_{1}=i \overline{ z }_{2}\) and \(\arg \left(\frac{ z _{1}}{\overline{ z }_{2}}\right)=\pi\). ThenJEE Mains 2022 Medium
More PYQs from JEE Mains
- If the solution of the differential equation \(\frac{d y}{d x}+e^{x}\left(x^{2}-2\right) y=\left(x^{2}-2 x\right)\left(x^{2}-2\right) e^{2 x} \quad\) satisfies \(y(0)=0\), then the value of \(y(2)\) isJEE Mains 2022 Medium
- If \(f\left( x \right) = {\left( {\frac{3}{5}} \right)^x} + {\left( {\frac{4}{5}} \right)^x} - 1\) , \(x \in R\) , then the equation \(f(x) = 0\) hasJEE Mains 2014 Hard
- If \(y=\cos \left(\frac{\pi}{3}+\cos ^{-1} \frac{x}{2}\right)\), then \((x-y)^2+3 y^2\) is equal to _____.JEE Mains 2025 Medium
- The parabolas : \(a^2+2 b x+c y=0\) and \(d x^2+2 ex + fy =0\) intersect on the line \(y=1\). If \(a, b, c, d, e, f\) are positive real numbers and \(a , b , c\) are in \(G.P.\), thenJEE Mains 2023 Hard
- For the system of linear equations \(2 x-y+3 z=5\) \(3 x+2 y-z=7\) \(4 x+5 y+\alpha z=\beta\) Which of the following is NOT correct ?JEE Mains 2023 Hard
- The function \(f(x)=\frac{x}{x^2-6 x-16}, x \in \mathbb{R}-\{-2,8\}\)JEE Mains 2024 Hard