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Using principle of mathematical induction prove …

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Using principle of mathematical induction prove x + 4 x + 3x.,..,...............+(3 n-2) x=1/2n(3n-2)x

Posted by Amit 12 Science 5 years, 7 months ago

CBSE > Class 11 > Mathematics

1 answers

Shoaib Khan 5 years, 7 months ago

Let p(n): x+4x+7x+........+(3n-2)x=1/2n(3n-2)x P(1): x=(3*1-2) x=x, so p(1) is true Now , assume that p(k) is also true for some integer k P(k): x+4x+7x+........+(3k-2)x=1/2k(3k-2)x Now , put n=k+1 P(k+1): x+4x+7x+........+(3k-2)x+{3(k+1)-2}x=1/2(k+1){3(k+1)-2}x LHS: x+4x+7x+.......+(3x-2)x+(3k+1)x From above equation 1/2k(3k-2)x+(3k+1)x Taking LCM and solving 1/2(k+1){3(k+1)-2}x....RHS.... hence proof

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