WBJEE · Maths · Sequences and Series
The sum of the series \(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}-\ldots . \infty\) is
- A \(2 \log _{\mathrm{e}} 2+1\)
- B \(2 \log _{\mathrm{e}} 2\)
- C \(2 \log _{\mathrm{e}} 2-1\)
- D \(\log _e 2-1\)
Answer & Solution
Correct Answer
(C) \(2 \log _{\mathrm{e}} 2-1\)
Step-by-step Solution
Detailed explanation
\begin{aligned}\text {Hints: } & s=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4} \ldots \ldots \infty \\ = & \left(\frac{1}{1}-\frac{1}{2}\right)-\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right) \ldots . \\ = &…
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 \((\alpha+\sqrt{\beta})\) and \((\alpha-\sqrt{\beta})\) are the roots of the equation \(x^{2}+p x+q=0,\) where \(\alpha, \beta, p\) and \(q\) are real, then the roots of the equation \(\left(p^{2}-4 q\right)\left(p^{2} x^{2}+4 p x\right)-16 q=0\) areWBJEE 2012 Medium
- Let \(\cos ^{-1}\left(\frac{y}{b}\right)=\log \left(\frac{x}{n}\right)^{n}\). ThenWBJEE 2020 Hard
- Let \(f:R\rightarrow R\) be defined as
\(f(x)=\left\{\begin{array}{lr}0, & x \text { is irrational} \\ \sin |x|, & x \text { is rational }\end{array}\right.\) Then, which of the following is true?WBJEE 2015 Easy - \(\lim _{x \rightarrow 0}(\sin x)^{2 \tan x}\) is equal toWBJEE 2017 Medium
- Let \(S\) denote the sum of the infinite series \(1+\frac{8}{2 !}+\frac{21}{3 !}+\frac{40}{4 !}+\frac{65}{5 !}+\ldots .\) ThenWBJEE 2014 Hard
- Let \(\cos ^{-1}\left(\frac{y}{b}\right)=\log _e\left(\frac{x}{n}\right)^n\), then \(A y_2+B y_1+C y=0\) is possible forWBJEE 2023 Hard
More PYQs from WBJEE
- Let \(f(x)=x^m, m\) being a non-negative integer. The value of \(m\) so that the equality \(f^{\prime}(a+b)=f^{\prime}(a)+f^{\prime}(b)\) is valid for all \(a\), \(b > 0\) isWBJEE 2023 Medium
- If \(|z-25 i| \leq 15\), then Maximum \(\arg (z)-\) Minimum \(\arg (z)\) is equal toWBJEE 2022 Medium
- Find the maximum value of \(|z|\) when \(\left|z-\frac{3}{z}\right|=2,\) where \(z\) being a complex number.WBJEE 2015 Easy
- If \({ }^9 P_5+5 .{ }^9 P_4={ }^{10} P_r\), then the value ' \(r\) ' isWBJEE 2025 Easy
- Three capacitors \(3 \mu \mathrm{F}, 6 \mu \mathrm{F}\) and \(6 \mu \mathrm{F}\) are connected in aeries to a source of \(120 \mathrm{V}\). The potential difference, in volt, across the \(3 \mu \mathrm{F}\) capacitor will beWBJEE 2014 Easy
- The equation of the tangent to the conic \(x^2-y^2-8 x+2 y+11=0\) at \((2,1)\) isWBJEE 2009 Medium