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, ...`
Advertisements
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 20 terms in the geometric progression 0.15, 0.015, 0.0015,…
If a, b, c and d are in G.P. show that (a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2 .
Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P2Rn = Sn
If the pth and qth terms of a G.P. are q and p, respectively, then show that (p + q)th term is \[\left( \frac{q^p}{p^q} \right)^\frac{1}{p - q}\].
Find three numbers in G.P. whose sum is 38 and their product is 1728.
Find the sum of the following geometric progression:
1, 3, 9, 27, ... to 8 terms;
Find the sum of the following geometric series:
(x +y) + (x2 + xy + y2) + (x3 + x2y + xy2 + y3) + ... to n terms;
Evaluate the following:
\[\sum^{10}_{n = 2} 4^n\]
Find the sum of the following serie:
5 + 55 + 555 + ... to n terms;
A person has 2 parents, 4 grandparents, 8 great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.
Find the sum of the following serie to infinity:
8 + \[4\sqrt{2}\] + 4 + ... ∞
Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.
The sum of three numbers a, b, c in A.P. is 18. If a and b are each increased by 4 and c is increased by 36, the new numbers form a G.P. Find a, b, c.
If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio is
If the first term of a G.P. a1, a2, a3, ... is unity such that 4 a2 + 5 a3 is least, then the common ratio of G.P. is
The fractional value of 2.357 is
If a, b, c are in G.P. and x, y are AM's between a, b and b,c respectively, then
The product (32), (32)1/6 (32)1/36 ... to ∞ is equal to
Mark the correct alternative in the following question:
Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a G.P. Then p2R3 : S3 is equal to
Check whether the following sequence is G.P. If so, write tn.
1, –5, 25, –125 …
Check whether the following sequence is G.P. If so, write tn.
`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5))`, ...
Check whether the following sequence is G.P. If so, write tn.
3, 4, 5, 6, …
If for a sequence, tn = `(5^("n"-3))/(2^("n"-3))`, show that the sequence is a G.P. Find its first term and the common ratio
The fifth term of a G.P. is x, eighth term of a G.P. is y and eleventh term of a G.P. is z verify whether y2 = xz
If p, q, r, s are in G.P. show that p + q, q + r, r + s are also in G.P.
The numbers x − 6, 2x and x2 are in G.P. Find 1st term
For a G.P. sum of first 3 terms is 125 and sum of next 3 terms is 27, find the value of r
For a G.P. If t3 = 20 , t6 = 160 , find S7
For a G.P. If t4 = 16, t9 = 512, find S10
Determine whether the sum to infinity of the following G.P.s exist, if exists find them:
`1/2, 1/4, 1/8, 1/16,...`
Express the following recurring decimal as a rational number:
`2.bar(4)`
Find : `sum_("r" = 1)^oo (-1/3)^"r"`
Answer the following:
Find five numbers in G.P. such that their product is 243 and sum of second and fourth number is 10.
Answer the following:
If p, q, r, s are in G.P., show that (p2 + q2 + r2) (q2 + r2 + s2) = (pq + qr + rs)2
Answer the following:
Find the sum of infinite terms of `1 + 4/5 + 7/25 + 10/125 + 13/6225 + ...`
Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a G.P. Then P2 R3 : S3 is equal to ______.
The third term of G.P. is 4. The product of its first 5 terms is ______.
If x, 2y, 3z are in A.P., where the distinct numbers x, y, z are in G.P. 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 ______.
The third term of a G.P. is 4, the product of the first five terms is ______.
