Question

s=1/1x4+1/4x7+1/7x10+...+1/94x97+1/97x100

 

Answer 1

\(S=\frac{1}{1\times4}+\frac{1}{4\times7}+\frac{1}{7\times10}+...+\frac{1}{94\times97}+\frac{1}{97\times100}\)

\(S=\frac{1}{3}\times\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{94}-\frac{1}{97}+\frac{1}{97}-\frac{1}{100}\right)\)

\(S=\frac{1}{3}\times\left(\frac{1}{1}-\frac{1}{100}\right)\)

\(S=\frac{1}{3}\times\frac{99}{100}\)

\(S=\frac{33}{100}\)