Arts (English Medium) Class 11 - CBSE Question Bank Solutions

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.

The ratio of the sum of the first three terms to that of the first 6 terms of a G.P. is 125 : 152. Find the common ratio.

The 4th and 7th terms of a G.P. are \[\frac{1}{27} \text { and } \frac{1}{729}\] respectively. Find the sum of n terms of the G.P.

Find the sum :

\[\sum^{10}_{n = 1} \left[ \left( \frac{1}{2} \right)^{n - 1} + \left( \frac{1}{5} \right)^{n + 1} \right] .\]

The fifth term of a G.P. is 81 whereas its second term is 24. Find the series and sum of its first eight terms.

If S₁, S₂, S₃ be respectively the sums of n, 2n, 3n terms of a G.P., then prove that \[S_1^2 + S_2^2\] = S₁ (S₂ + S₃).

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1)^th to (2n)^th term is \[\frac{1}{r^n}\].

If a and b are the roots of x² − 3x + p = 0 and c, d are the roots x² − 12x + q = 0, where a, b, c, d form a G.P. Prove that (q + p) : (q − p) = 17 : 15.