If a^{th} term of a series is \left ( 2a+1 \right )2^{-a} then sum of its infinite term is

  • Option 1)

    10

  • Option 2)

    8

  • Option 3)

    5

  • Option 4)

    0

 

Answers (1)

As we learnt in 

Sum of infinite terms of an AGP -

S_{\infty }= \frac{a}{1-r}+\frac{dr}{\left ( 1-r \right )^{2}}\\here \: \left | r \right |< 1

- wherein

a\rightarrow first term

d\rightarrow common diff. of a AP

r\rightarrow common ratio of a GP

 

 S_{\infty }=\frac{3}{2}+\frac{5}{2^{2}}+\frac{7}{2^{3}}+...........\infty \\*\\*\frac{S_{\infty }}{2}=\frac{3}{2^{2}}+\frac{5}{2^{3}}+...........\infty \\*\\*\frac{S_{\infty }}{2}=\frac{3}{2}+\frac{1}{2}+\frac{1}{2^{2}}+...........\infty \\*\\*\frac{S_{\infty }}{2}=\frac{3}{2}+1\\*\\*S_{\infty }=5


Option 1)

10

Incorrect

Option 2)

8

Incorrect

Option 3)

5

Correct

Option 4)

0

Incorrect

Exams
Articles
Questions