BITSAT2012MathematicsMathematical InductionActual
Let T (k) be the statement 1+3+5+ +(2 k-1)=k²+10 Which of the following is correct?
Options
- AT (1) is true
- BT (k) is true T (k+1) is true
- CT (n) is true for all n N
- DAll above are correct
Correct answer
B. T (k) is true T (k+1) is true
Step-by-step solution
When k =1, LHS =1 but RHS =1+10=11 T (1) is not true Let T (k) is true. That is array l 1+3+5+ .+(2 k-1)=k²+10 Now, 1+3+5+ . .+(2 k-1)+(2 k+1) =k²+10+2 k+1=(k+1)²+10 array T (k+1) is true. That is T (k) is true T (k+1) is true. But T (n) is not true for all n N , as T (1) is not true.