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प्रश्न
Find the sum of G.P. :
0.3 + 0.03 + 0.003 + 0.0003 + ........... to 8 items.
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उत्तर
Given G.P. : 0.3 + 0.03 + 0.003 + 0.003 + ...........
Here,
First term, a = 0.3
Common ratio, r = `0.03/0.3`= 0.1 ...(∵ r < 1)
Number of terms to be added, n = 8
∴ `S_n = (a(1 - r^n))/(1 - r)`
`=> S_8 = (0.3(1-(0.1)^8))/(1-0.1)`
= `(0.3(1 - (0.1)^8))/0.9`
=`(1 - (0.1)^8)/3`
= `1/3(1 - 1/10^8)`
संबंधित प्रश्न
Q 2
If a, b and c are in A.P, a, x, b are in G.P. whereas b, y and c are also in G.P.
Show that : x2, b2, y2 are in A.P.
If a, b, c are in G.P. and a, x, b, y, c are in A.P., prove that `a/x + c/y = 2`
Q 6
Find the sum of G.P. :
`1 - 1/3 + 1/3^2 - 1/3^3 + .........` to n terms.
Find the sum of G.P. :
`sqrt(3) + 1/sqrt(3) + 1/(3sqrt(3)) + ..........` to n terms.
Find the geometric mean between `4/9` and `9/4`
Q 7
Find the 5th term of the G.P. `5/2, 1, .........`
Find a G.P. for which the sum of first two terms is – 4 and the fifth term is 4 times the third term.
