Question

\(y=\frac{2}{1\cdot4}+\frac{2}{4\cdot7}+\frac{2}{7\cdot10}+....+\frac{2}{31\cdot34}\)     Y = ?

Answer 1

y = \(2\left(\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{31.31}\right)\)

 

3/2y =\(\frac{3}{2}.2\left(\frac{1}{1.4}+\frac{1}{4.7}+..+\frac{1}{31.34}\right)\)

\(\frac{3}{2}y=3\left(\frac{1}{1.4}+\frac{1}{4.7}+..+\frac{1}{31.34}\right)\)

\(\frac{3}{2}y=\frac{3}{1.4}+\frac{3}{4.7}+..+\frac{3}{31.34}=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+..+\frac{1}{31}-\frac{1}{34}\)]

3/2y = 1 - 1/34

3/2y = 33/34

y      = 33/34 : 3/2

y       =

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