Register

CAT 2003 | Question: 2-69

• edited by
1,850 views

1 Answer

Best answer
1 1 vote

S  = 1 + $\frac{4}{7}$ + $\frac{9}{7^{2}}$ + $\frac{16}{7^{3}}$ + $\frac{25}{7^{4}}$ +.................... (A)

$\frac{S}{7}$=       $\frac{1}{7}$ + $\frac{4}{7^{2}}$ + $\frac{9}{7^{3}}$ +    $\frac{16}{7^{4}}$ +.................... (B)

Substract equation (B) from (A),

$\frac{6S}{7}$ = 1 + $\frac{3}{7}$ + $\frac{5}{7^{2}}$ + $\frac{7}{7^{3}}$ + $\frac{9}{7^{4}}$  + ...................... (C)

$\frac{6S}{7^{2}}$=      $\frac{1}{7}$ + $\frac{3}{7^{2}}$ + $\frac{5}{7^{3}}$ + $\frac{7}{7^{4}}$  + ...................... (D)

Substract equation (D) from (C),

$\frac{36S}{49}$  = 1 + $\frac{2}{7}$ + $\frac{2}{7^{2}}$ + $\frac{2}{7^{3}}$ + $\frac{2}{7^{4}}$  + .................

$\frac{36S}{49}$  = 1 + $\frac{2 }{7}$ * $\frac{7 }{6}$

$\frac{36S}{49}$  = $\frac{4}{3}$

  S   = $\frac{4 * 49}{3* 36}$

  S   = $\frac{49}{27}$

Ans- C.

• selected by
Voting & Accepting an answer helps improve the community
← Previous · CAT 2003 | Question:...Next → · CAT 2003 | Question:...
← Previous in category · CAT 2003 | Question:...Next in category → · CAT 2003 | Question:...
Position:
Show:
Answer:

Related questions

0 0 votes
0 0 answers
949
949 views
go_editor asked Mar 2, 2016
949 views
CAT 2002 | Question: 73
Let $S=2x + 5x^2 + 9x^3 + 14x^4 + 20x^5 \dots \dots $ infinity. The coefficient of $n$-th term is$\frac{n(n+3)}{2}$. Then the sum $S$ is$\frac{x(2-x)}{(1-x)^3}$$\frac{(2-...
3 3 votes
1 1 answer
2.2k
2.2k views
go_editor asked Mar 16, 2020
2,222 views
CAT 2017 Set-2 | Question: 99
An infinite geometric progression $a_{1},a_{2},a_{3},\dots\dots$ has the property that $a_n =3(a_{n+1}+a_{n+2}+\dots\dots)$ for every $n\geq 1$. If the sum $a_{1}+a_{2}+a...
1 1 vote
1 1 answer
1.8k
1.8k views
Arjun asked Mar 1, 2020
1,825 views
CAT 2010 | Question: 10
Let $\text{S}$ denote the infinite sum $2+5x+9x^{2}+14x^{3}+20x^{4}+\ldots$where $\mid x \mid < 1$ and the coefficient of $x^{n-1}$ is $\dfrac{1}{2}n\left ( n+3 \right )...
1 1 vote
1 1 answer
2.0k
2.0k views
Misbah Ghaya asked Jun 22, 2024
1,997 views
CAT 2003 | Question: 2-65
Consider a cylinder of height $h$ cms and radius $r=\frac{2}{\pi}$ cms as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylind...
0 0 votes
1 answers 1 answer
5.4k
5.4k views
Lakshman Bhaiya asked Mar 31, 2022
5,432 views
CAT 2003 | Question: 2-64
Consider a cylinder of height $h$ cms and radius $r=\frac{2}{\pi}$ cms as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylind...