You visited us 1 times! Enjoying our articles? Unlock Full Access!

Sum of Infinite Terms

10.x, rs, x, ...

Question

10.x, rs, x,n terms (ifx # ± 1).

Open in App

Solution

The G.P. is x 3 , x 5 , x 7 ,…

Let the first term and common ratio of the given G.P. be a and r respectively.

Here,

a= x 3 r= x 5 x 3 = x 2

Here, r>1

The formula for the sum of first n terms of a G.P. for r>1 is given by,

S n = a( r n −1 ) r−1

Substitute the values of a and rin equation (1) to obtain the n th term.

S n = x 3 ( ( x 2 ) n −1 ) ( x 2 )−1 = x 3 ( x 2n −1 ) x 2 −1

Thus, the sum of n terms of the G.P. x 3 , x 5 , x 7 ,… is x 3 ( x 2n −1 ) x 2 −1 .

Suggest Corrections

Similar questions

\frac{1 + 3 + 5 + \dots upto n terms}{4 + 7 + 10 + \dots upto n terms} = \frac{20}{67 {log}_{10} x}

\frac{20}{7 {log}_{10} x}

n = {log}_{10} x + {log}_{10} x^{1 / 2} + {log}_{10} x^{1 / 4} + \dots . . \infty,

x

S_{n} = {cot}^{- 1} (3 x + \frac{2}{x}) + {cot}^{- 1} (6 x + \frac{2}{x}) + {cot}^{- 1} (10 x + \frac{2}{x}) + \dots + upto n terms,

x > 0 .

lim n \to \infty S_{n} = 1,

x

{(x - \frac{1}{x})}^{10}

{(1 - 2 x + x^{2})}^{n}

{(1 + 3 x + 3 x^{2} + x^{3})}^{2 n}

{(2 x - \frac{x^{2}}{4})}^{9}

{(x - \frac{1}{x})}^{2 n + 1}

{(\frac{x}{3} + 9 y)}^{10}

{(3 - \frac{x^{3}}{6})}^{7}

5 + 55 + 555 + \dots to n terms = \frac{5}{81} (10^{n + 1} + x + y n)

y - x

6^{t h}

(x + *)^{n}

^{n} C_{5} x^{n - 10}

*

Join BYJU'S Learning Program