অসীম জ্যামিতিক অগ্রগতি রয়েছে যার জন্য 27,8 এবং 12 এর তিনটি পদ (n...

It x\ a n d\ y vary inversely, fill in the following blanks: (i) x 12 16 ... 8 ... y ... 6 4 ... 0.25 (ii) x 16 32 8 128 y 4 ... ... 0.25 (iii) x, 9, ..., 81, 243 y, 27, 9, ..., 1

Most of the formulae are verified on the basis of induction method by putting n=1,2,…. 27^(n)-8^(n) is divisible by ("for "n in N) .

Statement 1: sum_(r=0)^n(r+1)^n c_r=(n+2)2^(n-1)dot Statement 2: sum_(r=0)^n(r+1)^n c_r=(1+x)^n+n x(1+x)^(n-1)dot (1) Statement 1 is false, Statement ( 2) (3)-2( 4) is true (6) Statement 1 is true, Statement ( 7) (8)-2( 9) (10) is true, Statement ( 11) (12)-2( 13) is a correct explanation for Statement 1 (15) Statement 1 is true, Statement ( 16) (17)-2( 18) (19) is true; Statement ( 20) (21)-2( 22) is not a correct explanation for Statement 1. (24) Statement 1 is true, Statement ( 25) (26)-2( 27) is false.

Statement 1: For every natural number ngeq2 , 1/(sqrt(1))+1/(sqrt(2))+...+1/(sqrt(n))>sqrt(n) . Statement 2: For every natural number ngeq2,""n(n+1)

(i) The sum of n terms of two arithmetic series are in the ratio of (7n+1)/(4n+27) . Find the ratio of their 11 th terms. (ii) The sum of n terms of arithmetic progressions are in the ratio (3n+8):(7n+15) . Find the ratio of their 12 th terms.