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CBSE Class 11-science Answered

By using principle of mathematical induction, prove that: 1 + 4 + 7 + --- + (3n - 2) =n(3n-1)
Asked by Topperlearning User | 14 May, 2014, 03:21: PM
answered-by-expert Expert Answer
Let the given statement is P(n)
P(n) = 1 + 4 + 7+ -----+ (3n - 2) =n(3n-1) ,nelement of
 For n = 1,   P (1) = 1 =(3-1)=1 which is true.
Assume that P(k) is true for some positive integers k
P(k): 1 + 4 + 7 + -----+ (3k - 2) =k(3k-1)
We shall prove that P(k + 1) is also true.
Now, we have
1 + 4 + 7 + ----- (3k - 2) + [3(k + 1) - 2]
k(3k-1) + [3(k + 1) - 2]
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 | 14 May, 2014, 05:21: PM
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