38. Find the wrong term in the given series A, E, I, N, Q, U, Y OPTIONS = 1.N 2. I 3. Y 4. U

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\sqrt{2} + \frac{1}{\sqrt{2}} + \frac{1}{2 \sqrt{2}} + . . . to 8 terms;

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

\frac{3}{5} + \frac{4}{5^{2}} + \frac{3}{5^{3}} + \frac{4}{5^{4}} + . . . to 2 n terms;

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

\sqrt{7}, \sqrt{21}, 3 \sqrt{7}, . . . to n terms

Find the sum of the following geometric series :

(i) 0.15 + 0.015 + 0.0015 + ..... to 8 terms ;

(ii) $\sqrt{2} + \frac{1}{\sqrt{2}} + \frac{1}{2 \sqrt{2}} + . . . . .$ to 8 terms ;

(iii) $\frac{2}{9} - \frac{1}{3} + \frac{1}{2} - \frac{3}{4} + . . . . .$ to 5 terms.

(iv) $(x + y) + (x^{2} + x y + y^{2}) + (x^{3} + x^{2} y + x y + y^{3}) + . . . .$ to n terms ;

(v) $\frac{3}{5} + \frac{4}{5^{2}} + \frac{3}{5^{3}} + \frac{4}{5^{4}} + . . . . .$ to 2n terms ;

(vi) $\frac{a}{1 + i} + \frac{a}{(1 + i)^{2}} + \frac{a}{(1 + i)^{3}} + . . . . + \frac{a}{(1 + i)^{n}}$

(vii) $1, - a, a^{2}, - a^{3}, . . . . . . . .$ to n terms $(a \neq 1)$

(viii) $x^{3}, x^{5}, x^{7}, . . . .$ to n terms

(ix) $\sqrt{7}, \sqrt{21}, 3 \sqrt{7}, . . . .$ to n terms

n

n^{t h}

(n^{2} + 5 n + 4) (n^{2} + 5 n + 8)

n

S_{n} = 3 n^{2} + 5 n

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