Question

When simplified, the product (2-1/3) (2-3/5) (2-5/7)......(2-997/999) is equal to?

Answer 1

Given, (2 - 1/3)(2 - 3/5)(2 - 5/7).......(2 - 997/999)
Let P =
(2 - 1/3) = 5/3
(2 - 3/5) = 7/5
(2 - 5/7) = 9/7
.........
...............
(2 - 997/999) = (1998 - 997)/999 = 1001/999

P = (2 - 1/3)(2 - 3/5)(2 - 5/7).......(2 - 997/999)
= 5/3 × 7/5 × 9/7 × .......... 1001/999
= 1001/3

Hence, answer is 1001/3

Answer 2

solution:-

given by:-

》the product (2-1/3) (2-3/5) (2-5/7)......(2-997/999) is equal to = ?

now , we have

》=(2 - 1/3) × (2 - 3/5) × (2 - 5/7) × . . . × (2 - (2k-1)/(2k+1)) × . . . × (2 - 997/999)
$( \frac{6 - 1}{3}) \times ( \frac{10 - 3}{5} ) \times ( \frac{14 - 5}{7} ).......$

》= 5/3 × 7/5 × 9/7 ×11/9 × . ... . × (2k+3)/(2k+1) ×.............. ×1001/999 

》=(1001/3) ans

☆ i hope its help☆