Advertisements
Advertisements
Question
Determine whether the sum to infinity of the following G.P.s exist, if exists find them:
`1/5, (-2)/5, 4/5, (-8)/5, 16/5, ...`
Solution
`1/5, (-2)/5, 4/5, (-8)/5, 16/5, ...`
`"a" = 1/5, "r" = ((-2)/5)/(1/5)` = – 2
Since, | r | = | – 2 | > 1
∴ Sum to infinity does not exist.
APPEARS IN
RELATED QUESTIONS
Find the sum to n terms of the sequence, 8, 88, 888, 8888… .
Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1)th to (2n)th term is `1/r^n`.
If f is a function satisfying f (x +y) = f(x) f(y) for all x, y ∈ N such that f(1) = 3 and `sum_(x = 1)^n` f(x) = 120, find the value of n.
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 :
nth term of the G.P.
\[\sqrt{3}, \frac{1}{\sqrt{3}}, \frac{1}{3\sqrt{3}}, . . .\]
If 5th, 8th and 11th terms of a G.P. are p. q and s respectively, prove that q2 = ps.
Find the sum of the following geometric series:
0.15 + 0.015 + 0.0015 + ... to 8 terms;
The sum of n terms of the G.P. 3, 6, 12, ... is 381. Find the value of n.
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 ratio of the sum of first three terms is to that of first 6 terms of a G.P. is 125 : 152. Find the common ratio.
Find the sum :
\[\sum^{10}_{n = 1} \left[ \left( \frac{1}{2} \right)^{n - 1} + \left( \frac{1}{5} \right)^{n + 1} \right] .\]
Find the sum of the following serie to infinity:
`2/5 + 3/5^2 +2/5^3 + 3/5^4 + ... ∞.`
Express the recurring decimal 0.125125125 ... as a rational number.
Find the rational numbers having the following decimal expansion:
\[0 . \overline3\]
If a, b, c, d are in G.P., prove that:
\[\frac{ab - cd}{b^2 - c^2} = \frac{a + c}{b}\]
If a, b, c are in G.P., prove that the following is also in G.P.:
a3, b3, c3
If pth, qth, rth and sth terms of an A.P. be in G.P., then prove that p − q, q − r, r − s are in G.P.
If a, b, c are in A.P. and a, b, d are in G.P., show that a, (a − b), (d − c) are in G.P.
Find the geometric means of the following pairs of number:
a3b and ab3
If (p + q)th and (p − q)th terms of a G.P. are m and n respectively, then write is pth term.
Given that x > 0, the sum \[\sum^\infty_{n = 1} \left( \frac{x}{x + 1} \right)^{n - 1}\] equals
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 5thhour?
The numbers 3, x, and x + 6 form are in G.P. Find nth term
The numbers x − 6, 2x and x2 are in G.P. Find x
For the following G.P.s, find Sn
0.7, 0.07, 0.007, .....
For the following G.P.s, find Sn.
`sqrt(5)`, −5, `5sqrt(5)`, −25, ...
For a G.P. If t4 = 16, t9 = 512, find S10
Find: `sum_("r" = 1)^10(3 xx 2^"r")`
Find : `sum_("n" = 1)^oo 0.4^"n"`
If the A.M. of two numbers exceeds their G.M. by 2 and their H.M. by `18/5`, find the numbers.
Answer the following:
Find `sum_("r" = 1)^"n" (2/3)^"r"`
At the end of each year the value of a certain machine has depreciated by 20% of its value at the beginning of that year. If its initial value was Rs 1250, find the value at the end of 5 years.
In a G.P. of positive terms, if any term is equal to the sum of the next two terms. Then the common ratio of the G.P. is ______.
The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm3 and the total surface area is 252cm2. The length of the longest edge is ______.
