Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from
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\[{{(n~+\text{ }1)}^{th}}~to\text{ }{{(2n)}^{th~}}term\text{ }i{{s}^{~}}\]$\tfrac{1}{{{r}^{n}}}$