Question

Show that  `(1xx2^2 + 2xx3^2 + ...+nxx(n+1)^2)/(1^2 xx 2 + 2^2 xx3 + ... + n^2xx (n+1))` = `(3n + 5)/(3n + 1)`

Answer 1

n^th term of the numerator = n(n + 1)² = n³ + 2n² + n

n^th term of the denominator = n²(n + 1) = n³ + n²