1/1x4 + 1/4x7 + 1/7x10 + ... + 1/97x100
= 1/3(3/1x4 + 3/4x7 + 3/7x10 + ... + 3/97x100)
= 1/3(1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + .... + 1/97 - 1/100)
= 1/3(1 - 1/100)
= 1/3*99/100
= 33/100
\(\frac{1}{1\times4}+\frac{1}{4\times7}+\frac{1}{7\times10}+....+\frac{1}{97\times100}\)
\(=\frac{1}{3}\times\left[\left(\frac{1}{1}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{7}\right)+.....+\left(\frac{1}{97}-\frac{1}{100}\right)\right]\)
\(=\frac{1}{3}\times\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+......+\frac{1}{97}-\frac{1}{100}\right)\)
\(=\frac{1}{3}\times\left(\frac{1}{1}-\frac{1}{100}\right)\)
\(=\frac{1}{3}\times\frac{99}{100}\)
\(=\frac{33}{100}\)
