AptiDude AptiDude

The value of 1 + ( 1 + 1 3 ) 1 4 + ( 1 + 1 3 + 1 9 ) 1 16 + ( 1 + 1 3 + 1 9 + 1 27 ) 1 64 + ⋯ 1 + \left(1 + \frac{1}{3}\right)\frac{1}{4} + \left(1 + ...

CAT Hard Sequence & Series (AP, GP, HP) MCQ

Question

The value of

1+(1+13)14+(1+13+19)116+(1+13+19+127)164+⋯1 + \left(1 + \frac{1}{3}\right)\frac{1}{4} + \left(1 + \frac{1}{3} + \frac{1}{9}\right)\frac{1}{16} + \left(1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27}\right)\frac{1}{64} + \cdots
is:

Options

A.
1513\frac{15}{13}
B.
1611\frac{16}{11}
C.
2712\frac{27}{12}
D.
158\frac{15}{8}
cat 2023infinite seriesgeometric progressionsummation

Solve This Question

Get instant feedback with detailed step-by-step solution

Start Solving →

Continue Practicing

Similar Questions

CAT Easy

Suppose $$ x_1, x_2, x_3, \dots, x_{100} $$ are in arithmetic progression such that $$ x_5 = -4 $$ a...
CAT Hard

Consider the sequence $$ t_1 = 1 $$, $$ t_2 = -1 $$, and $$ t_n = \left(\frac{n-3}{n-1}\right) t_...
CAT Hard

The sum of the infinite series $$ \frac{1}{5} \left( \frac{1}{5} - \frac{1}{7} \right) + \left( \...
CAT Medium

For some positive and distinct real numbers $$ x $$, $$ y $$, and $$ z $$, if $$ \frac{1}{\sqrt{x...
CAT Medium

A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on t...
CAT Medium

Let both the series $$a_1, a_2, a_3, \dots$$ and $$b_1, b_2, b_3, \dots$$ be in arithmetic progress...