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CBSE Class 11-commerce Answered

proove by PMI that 1+ 1+2/2 +1+2+3/2 +----------------+1+2+--------n/n= n(n+3/4) please solve this question and explain 3rd step properly
Asked by deepakagarwal1024 | 12 Jun, 2018, 06:42: PM
answered-by-expert Expert Answer
begin mathsize 16px style 1 plus fraction numerator 1 plus 2 over denominator 2 end fraction plus fraction numerator 1 plus 2 plus 3 over denominator 3 end fraction plus..... plus fraction numerator 1 plus 2 plus 3 plus.. plus straight n over denominator straight n end fraction equals fraction numerator straight n open parentheses straight n plus 3 close parentheses over denominator 4 end fraction straight n equals 1 lhs equals 1 rhs equals 1 let space straight n equals straight k space be space true so 1 plus fraction numerator 1 plus 2 over denominator 2 end fraction plus fraction numerator 1 plus 2 plus 3 over denominator 3 end fraction plus..... plus fraction numerator 1 plus 2 plus 3 plus.. plus straight k over denominator straight k end fraction equals fraction numerator straight k open parentheses straight k plus 3 close parentheses over denominator 4 end fraction now space straight n equals straight k plus 1 RHS thin space should space be space fraction numerator open parentheses straight k plus 1 close parentheses open parentheses straight k plus 4 close parentheses over denominator 4 end fraction LHS colon space 1 plus fraction numerator 1 plus 2 over denominator 2 end fraction plus fraction numerator 1 plus 2 plus 3 over denominator 3 end fraction plus..... plus fraction numerator 1 plus 2 plus 3 plus.. plus straight k plus 1 over denominator straight k plus 1 end fraction equals 1 plus fraction numerator 1 plus 2 over denominator 2 end fraction plus fraction numerator 1 plus 2 plus 3 over denominator 3 end fraction plus..... plus fraction numerator 1 plus 2 plus 3 plus.. plus straight k over denominator straight k end fraction plus fraction numerator 1 plus 2 plus 3 plus.. plus straight k plus 1 over denominator straight k plus 1 end fraction equals fraction numerator straight k open parentheses straight k plus 3 close parentheses over denominator 4 end fraction plus fraction numerator 1 plus 2 plus 3 plus.. plus straight k plus 1 over denominator straight k plus 1 end fraction equals fraction numerator straight k open parentheses straight k plus 3 close parentheses over denominator 4 end fraction plus fraction numerator open parentheses straight k plus 2 close parentheses open parentheses straight k plus 1 close parentheses over denominator 2 open parentheses straight k plus 1 close parentheses end fraction...... open parentheses 1 plus 2 plus 3 plus 4 plus.. plus straight n equals fraction numerator straight n open parentheses straight n plus 1 close parentheses over denominator 2 end fraction close parentheses equals fraction numerator straight k open parentheses straight k plus 3 close parentheses plus 2 straight k plus 4 over denominator 4 end fraction equals fraction numerator straight k squared plus 5 straight k plus 4 over denominator 4 end fraction equals fraction numerator open parentheses straight k plus 1 close parentheses open parentheses straight k plus 4 close parentheses over denominator 4 end fraction hence space proved end style
Answered by Arun | 14 Jun, 2018, 10:05: AM

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