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Statement 1 The difference between the sum of the first 100 even natural numbers and the sum of the first 100 odd natural numbers is 100. Statement 2 The difference between the sum opf the first n even natural numbers and sum of the first n odd natural numbers is n.A. Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1B. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1C. Statement 1 is true, Statement 2 is falseD. Statement 1 is false, Statement 2 is true |
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Answer» Correct Answer - A Statement 1 Sum of first 100 even natural numbers `E_(1)=2+4+"…"+200=(2(100xx101))/(2)=10100` Sum of 100 odd natural numbers `=1+3+"….."+199` `O=(100)/(2)(1+199)=10000` `:.E-O=100` So, Statement 1 is true. Statement 2 Sum of first n natural even numbers `E=2+4+"....."+2n=(2n(n+1))/(2)=n^(2)+n` Sum of first n odd natural numbers `O=1+3+"....."+(2n-1)` `=(n)/(2)[1=2n-1]=n^(2)` So, `E-O=n^(2)=n-n^(2)=n` Statement 2 is true and correct explanation for Statement 1. |
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