Find the sum of the following geometric series : (i) 0.15 + 0.015 + 0.

1.	Find the sum of the following geometric series : (i) 0.15 + 0.015 + 0.0015 + ..... to 8 terms ; (ii) √2+1√2+12√2+..... to 8 terms ; (iii) 29−13+12−34+..... to 5 terms. (iv) (x+y)+(x2+xy+y2)+(x3+x2y+xy+y3)+.... to n terms ; (v) 35+452+353+454+..... to 2n terms ; (vi) a1+i+a(1+i)2+a(1+i)3+....+a(1+i)n (vii) 1,−a,a2,−a3,........ to n terms (a≠1) (viii) x3,x5,x7,.... to n terms (ix) √7,√21,3√7,.... to n terms
Answer» 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

Find the sum of the following geometric series : (i) 0.15 + 0.015 + 0.0015 + ..... to 8 terms ; (ii) √2+1√2+12√2+..... to 8 terms ; (iii) 29−13+12−34+..... to 5 terms. (iv) (x+y)+(x2+xy+y2)+(x3+x2y+xy+y3)+.... to n terms ; (v) 35+452+353+454+..... to 2n terms ; (vi) a1+i+a(1+i)2+a(1+i)3+....+a(1+i)n (vii) 1,−a,a2,−a3,........ to n terms (a≠1) (viii) x3,x5,x7,.... to n terms (ix) √7,√21,3√7,.... to n terms

Answer»

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