InterviewSolution
Saved Bookmarks
| 1. |
1 +(2)/(4)+(2.5)/(4.8)+ (2.5.8)/(4.8.12) + (2.5.8.11)/(4.8.12.16)+ …isequal to |
|
Answer» `4^(-2//3 ) ` `(1 + x )^n= 1+ (nx )/(1 ! )+ (n (n - 1 ))/(2 ! ) x ^ 2+(n(n - 1 ) (n - 2 )) /(3! ) x ^ 3+ … ` On comparingthe abovetwoexpansions with , we get, `therefore(nx )/( 1! )= (2 )/(4)"" `...(1) ` (n(n - 1 ))/(2 ! ) x ^ 2= (2.5)/(4.8)"" `...(2) ` (n(n - 1 )(n - 2 ))/(3 ! ) x ^ 3= (2.5.8)/(4.8.12) "" `...(3) (2)` div`(1) ` ((n-1))/(2)x= (5)/(8)RARR(n-1)n =(5 )/(4) "" `...(4) `(3)div(2) ` ` ((n-2) x )/(3)=(8)/(12)rArr(n-2 ) x= 2 "" ...(5) ` ` (4) -(5) ` `x =(5)/(4)- 2` `x = (-3)/(4) ` `therefore((n-1))/(2)((-3)/(2))=(5)/(8) ` `thereforen =(-2)/(3) ` `therefore1 +(2)/(4)+(2.5)/(4.8)+ (2.5.8)/(4.8.12)+ ... =(1 - (3)/(4)) ^(-2/3) ` `= ((1)/(4)) ^(-2/3) ` `= 4 ^(2//3 ) ` `= 3sqrt(16)` |
|