JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Medium

1 of 1

Analyzing +4 | -1

Let

k

be natural number. Defined

S_k

as the sum of the infinite geometric series with first term

\left(k^2-1\right)

and common ratio

\frac{1}{k}

, that is

S_k=\frac{k^2-1}{k^0}+\frac{k^2-1}{k^1}+\frac{k^2-1}{k^2}+\ldots \ldots

. The value of

\sum\limits_{{k=1}}^{\infty} \frac{S_k}{2^{k-1}}

, is:

View answer and explanation

Correct option: D

Option D (14) is correct because it represents the sum of the series after correctly evaluating the geometric series and handling the case when k=1.

More Questions from SEQUENCE OF SERIES

Practice All Chapter MCQs →

A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\}

{A} \cup({B} \cap {C})

A-(B \cap C)

(B \cup C)-A

a,b,c

a,x,b

b,y,c

{x^2},{b^2},{y^2}

P(x)=1-x+x^2-x^3+\ldots+x^{2012}

y

Q(y)=a_0+a_1 y+\ldots+a_{2012} y^{2012}

y=x-2

\sum\limits_{{i=0}}^{2012} a_i

\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

\log \left(\frac{a}{3 b}\right)

A P

a, b

G P

a, b, c

\frac{3}{4}