Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Give an example of a statement P (n) which is true for all n. Justify your answer. Prove each of the statements in Exercises 3 to 16 by the Principle of Mathematical Induction.

Give an example of a statement P (n) which is true for all n. Justify your answer.
 

Answers (1)

P (n) is true for all n        …….. (Given)

Now, let P (n) be,

1+ 2 + 3 + 4 +... + n = n (n+1)/2\\ P (0) \rightarrow0 = 0(0+1)/2 = 0 \rightarrow true\\ P (1) \rightarrow1 = 1(2+2)/2 = 1 \rightarrow true\\ P (2) \rightarrow 1+2 = 2(2+1)/2 \rightarrow true\\ P (k) \rightarrow 1+2+3+... +k = k (k+1)/2\\ P (k+1) \rightarrow 1+2+3+... +k+1 = k (k+1)/2 + k + 1 = (k+1) (k+2)/2 \rightarrow p (k+1)

is true for all k

Thus, P (n) is true for all n.

Posted by

infoexpert21

View full answer

Similar Questions

Latest Question