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Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from
CBSE | Class 11 | Exercise 9.3 | Maths | NCERT | Sequences and Series
Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.3 - 28

SOLUTION:-

Let

    \[a\]

be the initial term and

    \[r\]

be the normal proportion of the G.P.

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.3 - 30

Since there are n terms from

    \[~{{(n~+1)}^{th}}~to\text{ }{{(2n)}^{th}}~term,\]

Amount of terms from

    \[{{(n~+\text{ }1)}^{th}}~to\text{ }{{(2n)}^{th}}~term\]

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.3 - 31

    \[a{{~}^{n~}}^{+1}~=~ar{{~}^{n\text{ }+\text{ }1}}{{~}^{\text{ }1}}~=~a{{r}^{n}}\]

Consequently, required proportion =

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.3 - 32

Consequently, the proportion of the amount of first

    \[n\]

terms of a G.P. to the amount of terms from

    \[{{(n~+\text{ }1)}^{th}}~to\text{ }{{(2n)}^{th~}}term\text{ }i{{s}^{~}}\]

\tfrac{1}{{{r}^{n}}}

i

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