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If (1 + i) (2 +i) (3 + i)…..(n+i)=a+ib ,...

If (1 + i) (2 +i) (3 + i)…..(n+i)=a+ib ,show that 2.5.10….`(n^2+1)=a^2+b^2`

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UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 4-EXERCISE
  1. Show that cos^6theta+sin^6theta=1/8(5+3cos4theta)

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  2. If n be an integer, then find the value of tan{(npi)/(2)+(-1)^(n).(pi...

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  3. If (1 + i) (2 +i) (3 + i)…..(n+i)=a+ib ,show that 2.5.10….(n^2+1)=a^2+...

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  4. If n is a even number, find the sum of the series upto n terms1^2-2^2+...

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  5. How many 5 digits telephone number can be formed from the digits from ...

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  6. Find the value of 3^2/3. 3^2/9. 3^2/27…..

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  7. If the gradiant of the line joining the points (2a, -2) and (1, -a)...

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  8. Find the ratio in which the plane 2x+3y+5z=1 divides the line segment ...

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  9. Evaluate:lim(xrarr0)sinx/x

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  10. Find the condition for the existance of lim(xrarr0)f(x)

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  11. Find the variance of 1, 2, 3, 4.

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  12. There are four letters and four envelops with proper address. Find the...

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  13. For any three sets A, B, C. prove that A xx (B cup C)=" (A xx B) cup(A...

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  14. If cos alpha = k cos beta Show that tan ((alpha+beta)/2)=(1-k)/(1+k)co...

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  15. Solve : sectheta-1=(sqrt2-1)tantheta

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  16. Prove by mathematical induction.1/1.3+1/3.5+1/5.7+....+1/((2n-1)(2n+1)...

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  17. How many different arragements of the letters of the word ALGEBRA can ...

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  18. If the sum of the n term of an AP is n^2 + 2n . which, term will ...

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  19. If z=x+iy and (z-i)/(z+1)is purely imaginary,then show that the point ...

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  20. The equation of the two adjacent sides of a parallelogram are 4x+ 5y =...

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