Consider a series `1/2+1/(2^2)+2/(2^3)+3/(2^4)+5/(2^5)+.............+(lambdan)/(2^n).` If `S_n` denotes its sum to `n` tems, then `S_n` cannot be

Options

A. 2
B. 3
C. 4
D. 5

Answer

A, B, C, D

Explanation

`:. S_(n)=(1)/(2)+(1)/(2^(2))+(2)/(2^(3))+(3)/(2^(4))+(5)/(2^(5))+"...."+(lambdan)/(2^(n))`
` =(3)/(4)+(1)/(4)((1)/(2)+(1)/(2^(2))+(2)/(2^(3))+(3)/(2^(4))+(5)/(2^(5))+"...."+(lambdan)/(2^(n))) +(1)/(2)((1)/(2)+(1)/(2^(2))+(2)/(2^(3))+"...."+(lambdan)/(2^(n))) -(1)/(4)-(lambda_(n))/(2^(n+2))-(lambda_(n))/(2^(n+1))`
`implies S_(n)=(3)/(4)+(1)/(4)S_(n)+(1)/(2)S_(n)-(1)/(4)-(lambda_(n))/(2^(n+2))-(lambda_(n))/(2^(n+1))`
`implies =(1)/(4)S_(n)=(1)/(2)-(lambda_(n))/(2^(n+2))-(lambda_(n))/(2^(n+1))implies S_(n)=2-(lambda_(n))/(2^(n+2))-(lambda_(n))/(2^(n-1))lt2`