Given-a-1-2-2-2-3-2-16-2-16-1-3-2-4-3-5-15-17-c-1-1-2-1-1-3-1-1-4-1-1-5-1-1-5-1-1-4-1-1-3-1-1-2-find-a-c-

Question Number 114638 by bobhans last updated on 20/Sep/20

G i v e n a = \frac{1^{2} + 2^{2} + 3^{2} + \dots + 16^{2} - 16}{1.3 + 2.4 + 3.5 + \dots + 15.17}

c = (1 - \frac{1}{2}) . (1 - \frac{1}{3}) . (1 - \frac{1}{4}) . (1 - \frac{1}{5}) .

(1 + \frac{1}{5}) (1 + \frac{1}{4}) (1 + \frac{1}{3}) (1 + \frac{1}{2}) .

f i n d a \times c =

Answered by bemath last updated on 20/Sep/20

(1) c = \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} \times \frac{6}{5} \times \frac{5}{4} \times \frac{4}{3} \times \frac{3}{2}

c = \frac{1}{5} \times \frac{6}{2} = \frac{3}{5}

a = \frac{\underset{k = 1}{\sum^{16}} k^{2} - 16}{\underset{k = 1}{\sum^{15}} k (k + 2)} = \frac{\frac{16.17.33}{6} - 16}{\frac{15.16.31}{6} + 2 (\frac{15.16}{2})}

= \frac{8.17.11 - 16}{5.8.31 + 15.16} = \frac{8 (17.11 - 2)}{5.8 (31 + 6)}

= \frac{185}{5.37} = 1

t h e n a \times c = 1 \times \frac{3}{5} = \frac{3}{5}

Commented by PRITHWISH SEN 2 last updated on 20/Sep/20

c = \frac{3}{5}