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If a1,a,a3...an are in A.P then prove th...

If `a_1,a_,a_3...a_n` are in A.P then prove that `a_1^2-a_2^2+a_3^2-a_4^2+....a_(2k-1)^2-a_(2k)^2= (k/(2k-1))(a_1^2-a_(2k)^2)`

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`a_(n)=(1)/(n(n+1)),S_(n)=1-(1)/((n+1),S_(prop)=1`
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Let the sequence a_1 , a_2 , a_3 ......... a_n form an A.P. then a_1^2 - a_2^2 + a_3^2 - a_4^2 +.....+ a_(2n-1)^2 - a_(2n)^2 is equal to:- (1) n/(2n-1)(a_1^2-a_(2n)^2) (2) (2n)/(n-1)(a_(2n)^2-a_1^2) (3) n/(n+1)(a_1^2+a_(2n)^2) (4)none of these

Let the sequence a_1 , a_2 , a_3 ......... a_n form an A.P. then a_1^2 - a_2^2 + a_3^2 - a_4^2 +.....+ a_(2n-1)^2 - a_(2n)^2 is equal to:- (1) n/(2n-1)(a_1^2-a_(2n)^2) (2) (2n)/(n-1)(a_(2n)^2-a_1^2) (3) n/(n+1)(a_1^2+a_(2n)^2) (4)none of these

If a_1,a_2,a_3,.....,a_n are in AP, prove that 1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+...+1/(a_(n-1)a_n)=(n-1)/(a_1a_n) .

If the nonzero numbers a_1,a_2,a_3,....,a_n are in AP, prove that 1/(a_1a_2a_3)+1/(a_2a_3a_4)+...+1/(a_(n-2)a_(n-1)a_n)=1/(2(a_2-a_1))(1/(a_1a_2)-1/(a_(n-1)a_n)) .

"If "a_1,a_2,a_3,.....,a_n" are in AP, prove that "a_(1)+a_(n)=a_(r)+a_(n-r+1)""

If a_1,a_2,……….,a_(n+1) are in A.P. prove that sum_(k=0)^n ^nC_k.a_(k+1)=2^(n-1)(a_1+a_(n+1))

If a_i>0, i=1, 2, 3,..., n then prove that a_1/a_2+a_2/a_3+a_3/a_4+...+a_(n-1)/a_n+a_n/a_1gen .

MOTION-SEQUENCE & SERIES -Exercise -3 Subjective /JEE Advanced
  1. The sum of first ten terms of an A.P. is 155 and the sum of first two ...

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  2. In a set of four number, the first three are in GP & the last three ar...

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  3. Find the 4^(th) term of an H.P., whose 7^(th) term is 1/20 and 13^(th)...

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  4. Find the sum of the n terms of the series whose nth term is (i) n(n+...

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  5. Find the sum of the series (5)/(13)+(55)/(13)^2+(555)/(13)^2+(5555)/((...

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  6. If the expression exp {1+|cosx|+cos^(3)x|+cos^(4)x+ . . . . oo)log(e...

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  7. The sum of the infinite series , 1^2- 2^2 / 5+ 3^2 / 5^2 - 4^2 / 5^3 +...

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  8. Find the sum of the n terms of the sequence 1/(1+1^2+1^4)+2/(1+2^2+2^...

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  9. Find the sum of the first n terms ofthe sequence : 1+2(1+1/n)+3(1+1/n)...

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  10. Find the n term and the sum to n terms of the sequence: (i) 1+5+13+29+...

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  11. If sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2)+1/(3^2))+sqrt(1+1/(3^2)+1/(4...

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  12. If a1,a,a3...an are in A.P then prove that a1^2-a2^2+a3^2-a4^2+....a(2...

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  13. If a, b, c, d, e be 5 numbers such that a, b, c are in AP, b, c, d, ar...

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  14. Using the relation A.M ge G.M. Prove that (i) tan theta +cot theta g...

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  15. Prove that b^2c^2+c^2a^2+a^2b^2gtabc(a+b+c), where a,b,c gt 0 .

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  16. The arithmetic mean of two numbers is 6 and their geometric mean G and...

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  17. In a circle of radius R a square is inscribed, then a circle is inscri...

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  18. 9. Find three numbers a,b,c between 2 & 18 such that; (G) their sum is...

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  19. Two distinct, real infinite geometric series each have a sum of 1 and ...

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  20. One of the roots of the equation 2000x^6 +100x^5 +10x^3+x-2=0 is the f...

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