Advertisements
Advertisements
प्रश्न
Find the rational form of the number `0.bar(123)`
उत्तर
Let x = 0.123123123 ... ⇒ x = `0.bar(123)` ...(1)
Multiplying 1000 on both rides
1000x = 123.123123 … ⇒ 1000x = `123 . bar(123)` ...(2)
(2) – (1) = 1000x – x `123.bar(123) - 0.bar(123)`
⇒ 999x = 123
⇒ x = `123/999`
⇒ x = `41/333` Rational number
APPEARS IN
संबंधित प्रश्न
Find the sum of first n terms of the G.P.
`5, -3, 9/5, - 27/25, ...`
Find the sum of first n terms of the G.P.
256, 64, 16, …
Find the sum to infinity of 9 + 3 + 1 + ….
Find the sum to infinity of `21 + 14 + 28/3 + ...`
Find the sum to n terms of the series
0.4 + 0.44 + 0.444 + …… to n terms
Find the sum to n terms of the series
3 + 33 + 333 + ………… to n terms
Find the sum of the Geometric series 3 + 6 + 12 + …….. + 1536
If Sn = (x + y) + (x2 + xy + y2) + (x3 + x2y + xy2 + y3) + ... n terms then prove that (x – y)Sn = `[(x^2(x^"n" - 1))/(x - 1) - (y^2(y^"n" - 1))/(y - 1)]`
A man saved ₹ 16500 in ten years. In each year after the first, he saved ₹ 100 more than he did in the preceding year. How much did he save in the first year?
Find the G.P. in which the 2nd term is `sqrt(6)` and the 6th term is `9sqrt(6)`
