Advertisements
Advertisements
प्रश्न
The fractional value of 2.357 is
विकल्प
(a) 2355/1001
(b) 2379/997
(c) 2355/999
(d) none of these
Advertisements
उत्तर
(c) \[\frac{2355}{999}\]
\[2 . \bar{{357}} = 2 . 0 + 0 . 357 + 0 . 000357 + 0 . 000000357 + . . . \infty \]
\[ \Rightarrow 2 . \bar{{357}} = 2 + \left[ \frac{357}{{10}^3} + \frac{357}{{10}^6} + \frac{357}{{10}^9} + . . . \infty \right]\]
\[ \Rightarrow 2 . \bar{{357}} = 2 + \frac{\frac{357}{{10}^3}}{1 - \frac{1}{{10}^3}}\]
\[ \Rightarrow 2 . \bar{{357}} = 2 + \frac{357}{999}\]
\[ \Rightarrow 2 . \bar{{357}} = \frac{2355}{999}\]
\[\]
संबंधित प्रश्न
The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7thterm.
Which term of the following sequence:
`2, 2sqrt2, 4,.... is 128`
Find the sum to n terms of the sequence, 8, 88, 888, 8888… .
Show that the products of the corresponding terms of the sequences a, ar, ar2, …arn – 1 and A, AR, AR2, … `AR^(n-1)` form a G.P, and find the common ratio
The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.
Find :
the 8th term of the G.P. 0.3, 0.06, 0.012, ...
Find :
the 12th term of the G.P.
\[\frac{1}{a^3 x^3}, ax, a^5 x^5 , . . .\]
The seventh term of a G.P. is 8 times the fourth term and 5th term is 48. Find the G.P.
If a, b, c, d and p are different real numbers such that:
(a2 + b2 + c2) p2 − 2 (ab + bc + cd) p + (b2 + c2 + d2) ≤ 0, then show that a, b, c and d are in G.P.
Find the sum of the following geometric series:
x3, x5, x7, ... to n terms
The common ratio of a G.P. is 3 and the last term is 486. If the sum of these terms be 728, find the first term.
The fifth term of a G.P. is 81 whereas its second term is 24. Find the series and sum of its first eight terms.
How many terms of the G.P. `3, 3/2, 3/4` ..... are needed to give the sum `3069/512`?
Prove that: (21/4 . 41/8 . 81/16. 161/32 ... ∞) = 2.
If Sp denotes the sum of the series 1 + rp + r2p + ... to ∞ and sp the sum of the series 1 − rp + r2p − ... to ∞, prove that Sp + sp = 2 . S2p.
Express the recurring decimal 0.125125125 ... as a rational number.
Find the rational numbers having the following decimal expansion:
\[0 . 6\overline8\]
Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.
If a, b, c are in G.P., prove that log a, log b, log c are in A.P.
If a, b, c are in G.P., prove that \[\frac{1}{\log_a m}, \frac{1}{\log_b m}, \frac{1}{\log_c m}\] are in A.P.
If a, b, c are in G.P., prove that:
a (b2 + c2) = c (a2 + b2)
If the fifth term of a G.P. is 2, then write the product of its 9 terms.
If pth, qth and rth terms of an A.P. are in G.P., then the common ratio of this G.P. is
Check whether the following sequence is G.P. If so, write tn.
3, 4, 5, 6, …
For the G.P. if r = − 3 and t6 = 1701, find a.
Find four numbers in G.P. such that sum of the middle two numbers is `10/3` and their product is 1
The number of bacteria in a culture doubles every hour. If there were 50 bacteria originally in the culture, how many bacteria will be there at the end of 5th hour?
The numbers x − 6, 2x and x2 are in G.P. Find x
Find: `sum_("r" = 1)^10(3 xx 2^"r")`
Find: `sum_("r" = 1)^10 5 xx 3^"r"`
If one invests Rs. 10,000 in a bank at a rate of interest 8% per annum, how long does it take to double the money by compound interest? [(1.08)5 = 1.47]
Determine whether the sum to infinity of the following G.P.s exist, if exists find them:
`2, 4/3, 8/9, 16/27, ...`
Find : `sum_("r" = 1)^oo 4(0.5)^"r"`
Select the correct answer from the given alternative.
If for a G.P. `"t"_6/"t"_3 = 1458/54` then r = ?
Answer the following:
Find three numbers in G.P. such that their sum is 35 and their product is 1000
Answer the following:
If for a G.P. first term is (27)2 and seventh term is (8)2, find S8
Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.
If the sum of an infinite GP a, ar, ar2, ar3, ...... . is 15 and the sum of the squares of its each term is 150, then the sum of ar2, ar4, ar6, .... is ______.
If the expansion in powers of x of the function `1/((1 - ax)(1 - bx))` is a0 + a1x + a2x2 + a3x3 ....... then an is ______.
