Sum of Infinite Terms of a GP
- circle whose centre is at (−12, −32).
- straight line whose slope is 32.
- circle whose diameter is √2.
- straight line whose slope is −23.
The value of 913.919.9127..... to ∞ is
For integers n and r, let...The maximum value of k for which the sum exists is equal to
In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then, the common ratio of this progression equals
The sum of an infinite G.P. is 4 and the sum of the cubes of its terms is 192. The common ratio of the original G.P. is
The fractional value of 2.357 is
none of these
Find the sum of the following series to infinity :
(iv) 10 - 9 + 8.1 - 7.29 + ...... ∞
Express the recurring decimal 0.125125125... as a rational number.
∣∣ ∣∣x+2x+3x+2ax+3x+4x+2bx+4x+5x+2c∣∣ ∣∣ is
The sum of first two terms of an infinite G.P. is 5 and each term is three times the sum of the succeeding terms. Find the G.P.
Given that x > 0, the sum ∑∞n=1(xx+1)n−1 equals
x + 1
Find the rotional number whose decimal expansion is 0.¯423.
Which term of the series ... is ?
Find the rational numbers having the following decimal expansions :
Find the geometric series whose and terms are and , respectively.
In an infinite geometric series, the first term is and the common ratio is . If the sum of the series is and the second term is , then is:
Robin bought a computer for . It will depreciate, or decrease in value, by each year that she owns it.
a) Is the sequence formed by the value at the beginning of each year arithmetic, geometric, or neither? Explain.
b) Write an explicit formula to represent the sequence.
c) Find the value of the computer at the beginning of the .
Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.
- None of the above