COMEDK2017MathematicsMathematical Induction
The statement P(n): ' 1 1 !+2 2 !+3 3 ! + +n n !=(n+1) !-1 is
Options
- Atrue for all n>1
- Bnot true for any n
- Ctrue for all n N
- DNone of these
Correct answer
C. true for all n N
Step-by-step solution
P(1): ' 1 1 !=(1+1) !-1 ' is true. Let P(k): ^ 1 1 !+2 2 !+3 3 !+ +k k !=(k+1) !-1^ is true. Now, P(k+1): 1 1 !+2 2 !+ array r +k+k !+(k+1) (k+1) ! array =(k+1) !-1+(k+1)(k+1) !=(k+1) !+(k+1) (k+1) !-1=(k+1) !(1+k+1)-1=(k+2) !-1 i.e., P(k) is true P(k+1) is true