Show that `ln(4xx12xx36xx108...` upto `n` terms) = `2nln2+(n(n-1))/2 ln3`

If (1 + 2 + 3 + 4 + 5 +………..upto n terms) / ( 1xx2 + 2xx3 + 3xx4 + 4xx5 + …. upto n terms) = 3/22 Find the value of n

Find 2 xx 6 + 4 xx 9 + 6 xx 12 + …… upto n terms.

Prove that 1^(1)xx2^(2)xx3^(3)xx xx n^(n)<=[(2n+1)/3]^(n(n+1)/2),n in N

If (1xx3 + 2xx5 + 3xx7 + ….. upto n terms) / ( 1^3 + 2^3 + 3^3 + …… upto n terms) = 5/9, find the value of n.

Show that (1 xx 2^(2) + 2 xx 3^(2) + . . . + n xx ( n + 1) ^(2))/( 1 ^(2) xx 2 + 2^(2) xx 3 + . . . + n^(2) xx ( n + 1) ) = ( 3 n + 5)/( 3 n + 1 )

Show that overset(2 n) C_n=(1 xx 3 xx 5 xx . . xx(2 n-1))/(n !) .2overset(n)

Show that (1 xx 2^(2) + 2 xx 3^(2) + ... +n xx (n + 1)^(2))/(1^(2) xx 2 + 2^(2) xx 3+ ... + n^(2) xx (n + 1)) = (3n + 5)/(3n + 1)