Advertisements
Advertisements
प्रश्न
Find the sum of G.P. :
`1 - 1/2 + 1/4 - 1/8 + ..........` to 9 terms.
उत्तर
Given G.P. : `1 - 1/2 + 1/4 - 1/8 + ..........`
Here,
First term, a = 1
Common ratio, r = `(-1/2)/1 = -1/2` ...(∵ r < 1)
Number of terms to be added, n = 9
∴ `S_n = (a(1 - r^n))/(1 - r)`
`=> S_8 = (1(1 - (-1/2)^9))/(1 - (-1/2))`
= `(1 - (-1/2)^9)/(1 + 1/2)`
= `(1 + 1/2^9)/(3/2)`
= `2/3(1 + 1/2^9)`
= `2/3(1 + 1/512)`
= `2/3 xx 513/512`
= `171/256`
APPEARS IN
संबंधित प्रश्न
Find, which of the following sequence from a G.P. :
`1/8, 1/24, 1/72, 1/216, ................`
Find the 9th term of the series :
1, 4, 16, 64, ...............
Which term of the G.P.:
`-10, 5/sqrt(3), -5/6,....` is `-5/72`?
The product of 3rd and 8th terms of a G.P. is 243. If its 4th term is 3, find its 7th term.
Find the seventh term from the end of the series :
`sqrt(2), 2, 2sqrt(2), ........., 32.`
Q 6
If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.
How many terms of the geometric progression 1 + 4 + 16 + 64 + …….. must be added to get sum equal to 5461?
Find the 5th term of the G.P. `5/2, 1, .........`
The first two terms of a G.P. are 125 and 25 respectively. Find the 5th and the 6th terms of the G.P.
