Commerce (English Medium) इयत्ता ११ - CBSE Question Bank Solutions

Find the sum of the following geometric series:

\[\frac{2}{9} - \frac{1}{3} + \frac{1}{2} - \frac{3}{4} + . . . \text { to 5 terms };\]

Find the sum of the following geometric series:

(x +y) + (x² + xy + y²) + (x³ + x²y + xy² + y³) + ... to n terms;

Find the sum of the following geometric series:

`3/5 + 4/5^2 + 3/5^3 + 4/5^4 + ....` to 2n terms;

Find the sum of the following geometric series:

\[\frac{a}{1 + i} + \frac{a}{(1 + i )^2} + \frac{a}{(1 + i )^3} + . . . + \frac{a}{(1 + i )^n} .\]

Find the sum of the following geometric series:

1, −a, a², −a³, ....to n terms (a ≠ 1)

Find the sum of the following geometric series:

x³, x⁵, x⁷, ... to n terms

Find the sum of the following geometric series:

`sqrt7, sqrt21, 3sqrt7,...` to n terms

Evaluate the following:

\[\sum^{11}_{n = 1} (2 + 3^n )\]

Evaluate the following:

\[\sum^n_{k = 1} ( 2^k + 3^{k - 1} )\]

Evaluate the following:

\[\sum^{10}_{n = 2} 4^n\]

Find the sum of the following serie:

5 + 55 + 555 + ... to n terms;

Find the sum of the following series:

7 + 77 + 777 + ... to n terms;

Find the sum of the following series:

9 + 99 + 999 + ... to n terms;

Find the sum of the following series:

0.5 + 0.55 + 0.555 + ... to n terms.

Find the sum of the following series:

0.6 + 0.66 + 0.666 + .... to n terms

How many terms of the G.P. 3, 3/2, 3/4, ... be taken together to make \[\frac{3069}{512}\] ?

How many terms of the sequence \[\sqrt{3}, 3, 3\sqrt{3},\]  ... must be taken to make the sum \[39 + 13\sqrt{3}\] ?

Show that \[\lim_{x \to 0} \frac{x}{\left| x \right|}\] does not exist.