`11-2=9=3^2 and 1111-22=1089=3 3^2` show that `((111111....1))/( 2n 1s)-((22222....2))/(n 2s)` is perfect square.

11-2=9=3^(2) and 1111-22=1089=33^(2) show that ((11111......))/(2n1s)-((222222...2))/(n2s) is perfect square.

Show that 1!+2!+3!+...+n! cannot be a perfect square for any n in N,n>=4

1.1!+2.2!+3.3!+.......n.n! is equal to

Show that lim_(n to infty)(1^2+2^2+...+(3n)^2)/((1+2+...+5n)(2n+3))=9/25

1+1.1!+2.2!+3.3!+......n.n! is equal to

1+1.1!+2.2!+3.3!+.......+n.n! is equal to

Let S_(n)=1+(1)/(2)+(1)/(3)+….+(1)/(n) Show that s_(n)=n-((1)/(2)+(2)/(3))+…….+(n-1)/(n)) .

Show that 1^3/1+(1^3+2^3)/(1+3)+............n "terms "=n/24(2n^2+9n+13)

S_(n) = (1+2+3+....+n)/( n) then S_(1)^(2) + S_(2)^(2) + S_(3)^(2) + ..... + S_(n)^(2) =

If S_(1), S_(2), S_(3),…., S_(n) are the sums to infinity of n infinte geometric series whose first terms are 1,2,3,… n and whose common ratios are (1)/(2), (1)/(3), (1)/(4), ….(1)/(n+1) respectively, show that, S_(1) + S_(2) + S_(3) +…S_(n) = (1)/(2)n(n+3)