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If `a_1,a_2,a_3, ,a_n` are in A.P., where `a_i >0` for all `i` , show that `1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_2)+sqrt(a_3))+ ..+1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))dot`

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If a_1,a_2,a_3, ,a_n are in A.P., where a_i >0 for all i , show that 1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_1)+sqrt(a_3))++1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))dot

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VMC MODULES ENGLISH-SEQUENCE AND SERIES -JEE MAIN & Advance ( ARCHIVE)
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  2. about to only mathematics

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  3. The real numbers x1, x2, x3 satisfying the equation x^3-x^2+b x+gamma=...

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  4. about to only mathematics

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  5. The number a, b and c are between 2 and 18, such that (i) their su...

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  6. Does there exist a geometric progression containing 27 and 8 and 12 as...

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  7. If the m th, n th and p th terms of an AP and GP are equal and are x ,...

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  8. about to only mathematics

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  9. If S(1), S(2), S(3),...,S(n) are the sums of infinite geometric series...

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  10. The sum of the squares of three distinct real numbers which are in G...

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  11. If a , b , c , are positive real numbers, then prove that (2004, 4M) {...

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  12. If a,b,c are in AP and a^(2),b^(2),c^(2) be in HP. Then, prove that -(...

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  13. If A1,A2 be two A.M.\'s G1,G2 be the two G.M.\'s and H1,H2 be the two ...

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  14. Let a(1), a(2)...be positive real numbers in geometric progression. Fo...

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  15. If x,y,z are in HP, then show that log(x+z)+log(x+z-2y)=2 log (x-z)

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  16. about to only mathematics

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  17. If a >0,b >0 and c >0 prove that (1984, 2M) (a+b+c)(1/a+1/b+1/c)geq9

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  18. If the sum of first n terms of an A P is c n^2, then the sum of square...

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  19. Let Sn=sum(k=1)^(4n)(-1)(k(k+1))/2k^2dot Then Sn can take value (s) 10...

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  20. Let f(x)=ax^2 + bx+c whose roots are alpha and beta , a ne 0 and tr...

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