" 13."quad (1-(1)/(2))(1-(1)/(3))(1-(1)/(4))cdots(1-(1)/(n+1))=(1)/(n+1)

prove that (1-(1)/(2^(2)))(1-(1)/(3^(2)))(1-(1)/(4^(2)))(1-(1)/(n^(2)))=(n+1)/(2n) for all natural numbers,n>=1(1-(1)/(n^(2)))=(n+1)/(2n)

For a positive integer n let a(n)=1+(1)/(2)+(1)/(3)+(1)/(4)cdots+(1)/((2^(n))-1). Then a(100) 100c.a(200)<=100d.a(200)<=100

For all quad prove that (1)/(1.2)+(1)/(2.3)+(1)/(3.4)+...+(1)/(n(n+1))=(n)/(n+1)

If S_(1), S_(2),cdots S_(n) , ., are the sums of infinite geometric series whose first terms are 1, 2, 3,…… ,n and common ratios are (1)/(2) ,(1)/(3),(1)/(4),cdots,(1)/(n+1) then S_(1)+S_(2)+S_(3)+cdots+S_(n) =

For all ngt=1 , prove that , (1)/(1.2) + (1)/(2.3) + (1)/(3.4) + ……+ (1)/(n(n+1)) = (n)/(n+1)

(1)/(n)+(1)/(n+1)+(1)/(n+2)++(1)/(2n-1)=1-(1)/(2)+( 1)/(3)-(1)/(4)++(1)/(2n-1)

Prove by the principle of mathematical induction that for all nN:(1)/(1.3)+(1)/(35)+(1)/(57)++(1)/((2n-1)(2n+1))=(n)/(2n+1)