Show that,`(1+5^(-1))(1+5^(-2))(1+5^(-4))(1+5^(-8))"....."(1+5^(-2n))=(5)/(4)(1-5^(-2(n+1)))`.

(5^(n)+5^(n-1))/(5^(n+1)-5^(n))

(1)/(5)+(1)/(2.5^(2))+(1)/(3.5^(3))+(1)/(4.5^(4))+.......=

Find the sum (1^(4))/(1xx3)+(2^(4))/(3xx5)+(3^(4))/(5xx7)+......+(n^(4))/((2n-1)(2n+1))

Show that : (^(4n)C_(2n))/(^(2n)C_n) = (1.3.5...(4n-1))/{1.3.5...(2n-1)}^2

4(4)/(5)-:{2(1)/(5)-(1)/(2)(1(1)/(4)-(1)/(4)-(1)/(5))}

Show that (.^(4n)C_(2n))/(.^(2n)C_(n))=(1.3.5......(4n-1))/({1.3.5......(2n-1)}^(2)) .

(1^(4))/(1.3)+(2^(4))/(3.5)+(3^(4))/(5.7)+......+(n^(4)) /((2n-1)(2n+1))=(n(4n^(2)+6n+5))/(48)+(n)/(16(2n+1))

lim_(n->oo) (1)/(n^(6)){(n+1)^(5)+(n+2)^(5)+...+(2n)^(5)}

Show that Lt_(ntooo)(3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=-20/7

1.3+3.5+5.7+......+(2n-1)(2n+1)=(n(4n^(2)+6n-1))/(3)