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CBSE Class 11-science Answered

Show by using principle of mathematical induction, prove that: 1 + 2 + 3 + -----+ n =
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer
Let the given statement is P(n)  
P(n) = 1 + 2 + 3 + --- + n =  
For n = 1,   P(1) = is true, since 1 =  
Assume that P(k) is true for some positive integer k, i.e.
1 + 2 + 3 + ---+ k =
We shall prove that P(k +1) is true, whenever P(k) is true.
We have, 1 + 2 + 3 + -----+ k + (k + 1) =   + (k + 1)
                                                              
Thus P(k +1) is true, whenever P(k) is true.
Hence from principle of mathematical induction, the statement P(n) is true for all natural numbers N.
Answered by | 04 Jun, 2014, 03:23: PM
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