"If "x=a+(a)/(r)+(a)/(r^(2))+...oo,y=b-(...

`"If "x=a+(a)/(r)+(a)/(r^(2))+...oo,y=b-(b)/(r)+(b)/(r^(2))-...oo,"and "z=c+(c)/(r^(2))+(c)/(r^(4))+...oo," then prove that "(xy)/(z)=(ab)/(c).`

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If x=a+(a)/(r)+(a)/(r^(2))+...oo,y=b-(b)/(r)+(b)/(r^(2))+...oo, and z=c+(c)/(r^(2))+(c)/(r^(4))+...oo prove that (xy)/(z)=(ab)/(c)

if r>1 and x=a+(a)/(r)+(a)/(r^(2))+.........oo,y=b-(b)/(r)+(b)/(r^(2))-(b)/(r^(2)) and z=c+(c)/(r^(2))+(c)/(r^(4))+............oo then (xy)/(z)

If r>1 and x=a+(a)/(r)+(a)/(r^(2))............,y=b+(b)/(r)+(b)/(r^(2))...... and z=b+(b)/(r)+(b)/(r^(2))+.......... Then value of (xy)/(z^(2)) is

If A=1+r^(2)+r^(2a)+...oo=a and B=1+r^(b)+r^(2b)+...oo=b then (a)/(b) is equal to

If A=1+r^(a)+r^(2a)+ to oo andB=1+r^(b)+r^(2b)+oo, prove that r=((A-1)/(A))^(1/a)=((B-1)/(B))^(1/b)

If z_(r)=cos((pi)/(3^(r)))+i sin((pi)/(3^(r))),r=1,2,3 prove that z_(1)z_(2)z_(3)z_(oo)=i

If a=sum_(n=r)^( oo)(1)/(r^(4)) then sum_(r=1)^(oo)(1)/((2r-1)^(4))=

Prove that : (r_1-r)/(a) +(r_2-r)/(b) = (c )/(r_3) .

CBSE COMPLEMENTARY MATERIAL-SEQUENCES AND SERIES -SECTION-C(SHORT anwer type )

If the continued product of three numbers in G.P. is 216 and the sum o...
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Find the sum to infinity of the series: 1+3/2+5/2^2+7/2^3+..........oo
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if A=1+r^a+r^(2a)+......... up to infinity then express r in terms of ...
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Find the sum of first n terms of the series 0.7 + 0.77 + 0.777 + …..
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"If "x=a+(a)/(r)+(a)/(r^(2))+...oo,y=b-(b)/(r)+(b)/(r^(2))-...oo,"and ...
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The sum of first three terms of a G.P. is 15 and sum of next three ter...
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Prove that 0.0031=7/225 [Hint: 0.031 = 0.03 + 0.001 + 0.0001 +.....Now...
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If a ,\ b\ c are in G.P., prove that the following are also in G.P.: a...
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If a ,\ b\ c are in G.P., prove that the following are also in G.P.: a...
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If a, b, c are in G.P. that the following are also in G.P. sqrt(a),sqr...
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If a, b, c are in A.P. that the following are also in A.P:(i)(1)/(bc),...
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If a,b,c are in A.P. prove that b+c,c+a,a+b are also in A.P.
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If a, b, c are in A.P. then prove that the following are also in A.P:(...
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"If " a^(2), b^(2), c^(2)" are in A.P., prove that "(1)/(b+c),(1)/(c+a...
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Show that 0. 3bar(56) =353/990
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Find the sum of n terms of series : 3 + 5 + 9 + 15 + 23 + ………… n terms
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Sum of n terms the series : 1^2-2^2+3^2-4^2+5^2-6^2+
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The fourth term of a G.P. is 4. Find product of its first seven terms.
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If A(1), A(2), A(3), A(4) are four A.M’s between1/2 and 3, then prove ...
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If S(n) denotes the sum of first n terms of an A.P. If S(2n) = 5(Sn), ...
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