Question

The value of 1/1*4+1/4*7+1/7*10+1/10*13+1/13*16

Answer 1

this is the answer of the question

Answer 2

Answer:

$\frac{13}{144}$

Step-by-step explanation:

$\frac{1}{1\times 4}+\frac{1}{4\times 7}+\frac{1}{7\times 10}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$

$\frac{1}{3}(\frac{3}{1\times 4}+\frac{3}{4\times 7}+\frac{3}{7\times 10}+\frac{3}{10\times 13}+\frac{3}{13\times 16})$

( by multiplying both numerator and denominator by 3 )

$\frac{1}{3}(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16})$

$\frac{1}{3}(1-\frac{1}{16})$

$\frac{1}{3}(\frac{16-1}{16})$

$\frac{1}{3}\times \frac{15}{16}$

$=\frac{15}{48}$

$=\frac{5}{16}$ ( by simplifying )