JEE Mains · Maths · STD 11 - 8. sequence and series
The sum of first \(20\) terms of the sequence \(0.7,0.77,0.777, . . . \) is
- A \(\frac{7}{{18}}\left( {179 - {{10}^{ - 20}}} \right)\)
- B \(\;\frac{7}{9}\left( {99 - {{10}^{ - 20}}} \right)\)
- C \(\;\frac{7}{{81}}\left( {179 + {{10}^{ - 20}}} \right)\)
- D \(\;\frac{7}{9}\left( {99 + {{10}^{ - 20}}} \right)\)
Answer & Solution
Correct Answer
(C) \(\;\frac{7}{{81}}\left( {179 + {{10}^{ - 20}}} \right)\)
Step-by-step Solution
Detailed explanation
\(\frac{7}{10}+\frac{77}{100}+\frac{777}{10^{3}}+\ldots \ldots .+u p\) to \(20\) terms \(=7\left[\frac{1}{10}+\frac{11}{100}+\frac{111}{10^{3}}+\ldots . . up \text { to } 20 \text { terms }\right]\)…
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 the system of linear equations \(2 x-3 y=\gamma+5\) ; \(\alpha x+5 y=\beta+1\), where \(\alpha, \beta, \gamma \in R\) has infinitely many solutions, then the value of \(|9 \alpha+3 \beta+5 \gamma|\) is equal toJEE Mains 2022 Medium
- The area of the region \(A\,\{ \,(x,y)\,\,:\,\,0\,\, \le \,y\, \le \,x\,\left| x \right|\, + \,1\) and \( - \,1\, \le \,x\, \le \,1\,\} \) in sq. units, isJEE Mains 2019 Hard
- Let \(f\) be a function such that \(f(x)+3 f\left(\frac{24}{x}\right)\) \(=4 x, x \neq 0\). Then \(f(3)+f(8)\) is equal toJEE Mains 2025 Easy
- \( \text { If } S(x)=(1+x)+2(1+x)^2+3(1+x)^3+\ldots . \) \( +60(1+x)^{60}, x \neq 0 \text {, and }(60)^2 S(60)=a(b)^b+b\) where \(a, b N\), then \((a+b)\) equal to ...............JEE Mains 2024 Hard
- Let \(\mathrm{C}\) be a circle with radius \(\sqrt{10}\) units and centre at the origin. Let the line \(x+y=2\) intersects the circle \(\mathrm{C}\) at the points \(\mathrm{P}\) and \(\mathrm{Q}\). Let \(\mathrm{MN}\) be a chord of \(C\) of length \(2\) unit and slope \(-1\) . Then, a distance (in units) between the chord \(PQ\) and the chord \(MN\) is :JEE Mains 2024 Hard
- The remainder when \((11)^{1011}+(1011)^{11}\) is divided by \(9\) isJEE Mains 2022 Hard
More PYQs from JEE Mains
- Let \(S=\{4,6,9\}\) and \(T=\{9,10,11, \ldots, 1000\}\). If \(A=\left\{a_{1}+a_{2}+\ldots+a_{k}: k \in N, a_{1}, a_{2}, a_{3}, \ldots, a_{k} \in S\right\}\) then the sum of all the elements in the set \(T - A\) is equal to \(......\)JEE Mains 2022 Hard
- \(\lim _{x \rightarrow 0} \frac{\sin ^{2}\left(\pi \cos ^{4} x\right)}{x^{4}}\) is equal to :JEE Mains 2021 Hard
- If \(f(t)=\int_0^\pi \frac{2 x d x}{1-\cos ^2 \sin ^2 x}, 0 < t < \pi\), then the value of \(\int_0^{\frac{\pi}{2}} \frac{\pi^2 d t}{f(t)}\) equals ..........JEE Mains 2024 Hard
- Let \(A =\left(\begin{array}{cc} m & n \\ p & q \end{array}\right), d =| A | \neq 0| A - d (\operatorname{Adj} A )|=0\). ThenJEE Mains 2023 Hard
- The number of common tangents, to the circles \(x^2+y^2-18 x-15 y+131=0\) and \(x^2+y^2-6 x-6 y-7=0\), is :JEE Mains 2023 Medium
- The integral \(80 \int_0^{\frac{\pi}{4}}\left(\frac{\sin \theta+\cos \theta}{9+16 \sin 2 \theta}\right) d \theta\) is equal to :JEE Mains 2025 Medium