" Prove that "log_(e)((n^(2))/(n^(2)-1))=(1)/(n^(2))+(1)/(2n^(4))+(1)/(3n^(6))+.....oo

Lt_(n rarr oo)[(1+(1)/(n^(2)))^((2)/(n^(2)))(1+(2^(2))/(n^(2)))^((4)/(n^(2)))(1+(3^(2))/(n^(2)))^((6)/(n^(2))).....(1+(n^(2))/(n^(2)))^((2n)/(n^(2)))]

Prove that : log_e(n+1)-log_e(n-1)=2[1/n+1/(3n^3)+1/(5n^5)+...]

Prove that (1)/(n!)+(1)/(2!(n-2)!)+(1)/(4!(n-4)!)+...=(1)/(n!)2^(n-1)

1+((log n)^(2))/(2!)+((Log n)^(4))/(4!)+...... oo =

Prove that : 1^(2)+2^(2)+3^(2)+...+n^(2)=(n(n+1)(2n+1))/(6)

Prove that 1^(2)+2^(2)+3^(2)+.....+n^(2)=(n(n+1)(2n+1))/6

Show that, lim_(n to oo)((1)/(n + 1)+(1)/(n+2)+…+(1)/(6n))=log 6 .

Show that lim_(n rarr oo)((1)/(n+1)+(1)/(n+2)+...+(1)/(6n))=log6

Evaluate lim_(n rarr oo)n[(1)/((n+1)(n+2))+(1)/((n+2)(n+4))++(1)/(6n^(2))]

lim_(n rarr oo)((4+3n+n^(6))^((1)/(3)))/(1+3n+2n^(2))