Show that `1 + 1/3 + (1.3)/(3.6) + (1.3.5)/(3.6.9) + ….. = sqrt3`

Show that + 1/4 + (1.3)/(4.8) + (1.3.5)/(4.8.12) + …….= sqrt2

Show that 1 + 1/2.(3/5) + (1.3)/(2.4) (3/5)^2 + (1.3.5)/(2.4.6) (3/5)^3 + …… = sqrt([5/2])

Sho that 3/6 + (3.5)/(6.9) + (3.5.7)/(6.9.12)+ ……..oo 3 sqrt3 - 4

If x = (1.3)/(3.6) + (1.3.5)/(3.6.9) + (1.3.5.7)/(3.6.9.12) + ….. then prove that 9x^2 + 24x = 11

If n is a non zero rational number then show that 1 + n/2 + (n (n - 1))/(2.4) + (n(n-1)(n - 2))/(2.4.6) + ….. = 1 + n/3 + (n (n + 1))/(3.6) + (n (n + 1) (n + 2))/(3.6.9) + ….

If y = (1)/(3) + (1*3)/(3 *6) + (1 * 3*5)/(3*6*9) +… then the value of y^(2) + 2y is a. 2 b.-2 c. 0 d . None of these

1/(1.2)+(1.3)/(1.2.3.4)+(1.3.5)/(1.2.3.4.5.6)+.....oo

Show that sqrt3 =1+ 1/3 +( 1/3 ).( 3/6 )+(1/3)*((3/6)*(5/9)*(7/12)+.......

If x = (1*3)/(3*6)+(1*3*5)/(3*6*9)+(1*3*5*7)/(3*6*9*12)+. . . to infinite terms, then 9x^(2) + 24 x =

Show that : (1)/(3-2sqrt(2))- (1)/(2sqrt(2)-sqrt(7)) + (1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5 .