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If a,b,c are in A.P. prove that b+c,c+a,...

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. prove that (i) b+c,c+a,a+b are also in A.P. (ii) 1/(sqrt(b)+sqrt(c)),1/(sqrt(c)+sqrt(a)),1/(sqrt(a)+sqrt(b)) are also in A.P.

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If (b+c)/(a),(c+a)/(b),(a+b)/(c) are in A.P.prove that :bc,ca,ab are in A.P.

If a^(2)(b+c),b^(2)(c+a),c^(2)(a+_b) are in in A.P. then prove that a, b, c, are also in A.P. or ab + bc + ca = 0.

In DeltaABC , a^(2),b^(2),c^(2) are in A.P. Prove that cotA, cotB, cotC are also in A.P.

If a,b,c are in G.P.prove that log a,log b,log c are in A.P.

If a,b,c are in A.P.then prove that the following are also in A.P.(1)/(sqrt(b)+sqrt(c)),(1)/(sqrt(c)+sqrt(a)),(1)/(sqrt(a)+sqrt(b))

if (1)/(b+c),(1)/(c+a),(1)/(a+b) are in A.P. prove that a^(2),b^(2),c^(2) are also in A.P.

If (b+c-a)/a,(c+a-b)/b,(a+b-c)/c are in A.P. Prove that 1/a,1/b,1/c are also inA.P

CBSE COMPLEMENTARY MATERIAL-SEQUENCES AND SERIES -SECTION-C(SHORT anwer type )
  1. If the continued product of three numbers in G.P. is 216 and the sum o...

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  2. Find the sum to infinity of the series: 1+3/2+5/2^2+7/2^3+..........oo

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  3. if A=1+r^a+r^(2a)+......... up to infinity then express r in terms of ...

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  4. Find the sum of first n terms of the series 0.7 + 0.77 + 0.777 + …..

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

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  6. The sum of first three terms of a G.P. is 15 and sum of next three ter...

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  7. Prove that 0.0031=7/225 [Hint: 0.031 = 0.03 + 0.001 + 0.0001 +.....Now...

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  8. If a ,\ b\ c are in G.P., prove that the following are also in G.P.: a...

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  9. If a ,\ b\ c are in G.P., prove that the following are also in G.P.: a...

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  10. If a, b, c are in G.P. that the following are also in G.P. sqrt(a),sqr...

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  11. If a, b, c are in A.P. that the following are also in A.P:(i)(1)/(bc),...

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  12. 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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  13. If a, b, c are in A.P. then prove that the following are also in A.P:(...

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  14. "If " a^(2), b^(2), c^(2)" are in A.P., prove that "(1)/(b+c),(1)/(c+a...

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  15. Show that 0. 3bar(56) =353/990

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  16. Find the sum of n terms of series : 3 + 5 + 9 + 15 + 23 + ………… n terms

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  17. Sum of n terms the series : 1^2-2^2+3^2-4^2+5^2-6^2+

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  18. The fourth term of a G.P. is 4. Find product of its first seven terms.

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  19. If A(1), A(2), A(3), A(4) are four A.M’s between1/2 and 3, then prove ...

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  20. If S(n) denotes the sum of first n terms of an A.P. If S(2n) = 5(Sn), ...

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