`1/(1xx2) + 1/(2xx3) + 1/(3xx4) + ...`

Find the sum 3/(1xx2)xx1/2+4/(2xx3)xx(1/2)^2+5/(3xx4)xx(1/2)^2+ ton terms.

Find the sum to n terms of the series : 1 xx 2 + 2 xx 3 + 3xx4 + 4xx5+. . . . . .

Find the sum of the series 2/(1xx2)+5/(2xx3)xx2+(10)/(3xx4)xx2^2+(17)/(4xx5)xx2^3+ ton terms.

Find the sum to n terms of the series : 1xx2xx3 + 2xx3xx4 + 3xx4xx5 + ...

1/3xx1/4xx1/3xx1/3

1+1/4 + (1xx3)/(4xx8) + (1xx3xx5)/(4xx8xx12) + "….." is equal to

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

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 )

Tell what property allows you to compute 1 /3 xx (6 xx 4/5) as ( 1/3 xx 6 ) xx 4/3.

Find the sum of the series: (1)/((1xx3))+(1)/((3xx5))+(1)/((5xx7))+...+(1)/((2n-1)(2n+1))