Answer to Question #106512 in Algebra for Aravind

Question

What's the value of 1/1×4+1/4×7+1/7×10+..........+1/16×19?

Answer 1

1/(1×4)+1/(4×7)+1/(7×10)+..........+1/(16×19)=1/(1×4)+ 1/(4×7)+1/(7×10)+1/(10×13)+1/(13×16)+1/(16×19)=1/3×(1/1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16+1/16-1/19)=1/3×(1/1-1/19)=1/3×(18/19)=6/19.

Answer: 6/19