AP EAMCET2002MathematicsBasics of Mathematics
1+ 1+2 2 ! + 1+2+2^2 3 ! + is equal to
Options
- Ae^2+e
- Be^2
- Ce^2-1
- De^2-e
Correct answer
D. e^2-e
Step-by-step solution
We have, gathered 1+ 1+2 2 ! + 1+2+2^2 3 ! + T_n= 1+2+2^2+ +2^ n-1 n ! = 1 (2^n-1 ) 2-1 n ! = 2^n-1 n ! T_n= 2^n n ! - 1 n ! S_n= T_n= 2^n n ! - 1 n ! gathered gathered = ( 1 1 + 2 1 ! + 2^2 2 ! + )- (1+ 1 1 ! + 1 2 ! + ) =e^2-e gathered