Question

1/1x3+1/2x4+1/3x5+1/4x6+...+1/10x12

Answer 1

1/1×3 + 1/2×4 + 1/3×5 +...+ 1/10×12

= (1/2)×(1 - 1/3) + (1/2)×(1/2 - 1/4) + ...+ (1/2)(1/10 - 1/12)

= (1/2)×(1 - 1/3 + 1/2 - 1/4 + ...+ 1/10 - 1/12)

= (1/2)×(1 + 1/2 - 1/11 - 1/12)

= (1/2)×175/132

= 175/264