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sum(r=1)^nr^2-sum(m=1)^nsum(r=1)^mr is e...

`sum_(r=1)^nr^2-sum_(m=1)^nsum_(r=1)^mr` is equal to

A

0

B

`1/2(sum_(r=1)^nr^2+sum_(r=1)^n)`

C

`1/2(sum_(r=1)^nr^2-sum_(r=1)^nr)`

D

none of these

Text Solution

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The correct Answer is:
A
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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. Let Sk=underset(nrarrinfty)limsum(i=0)^n1/(k+1)^i. Then sum(k=1)^nkSk...

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  2. If a1,a2,a3...an are in HP and f(k)=sum(r=1)^nar-ak, then a1/(f(1)),a...

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  3. sum(r=1)^nr^2-sum(m=1)^nsum(r=1)^mr is equal to

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  4. The sum of the integer from 1 to 100 which is not divisible by 3 or 5 ...

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  5. If ab^2c^3,a^2b^3c^4,a^3b^4c^5 are in AP (a,b,cgt0) thgen the minimum...

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  6. If the sum of n terms of the series 1/1^3+(1+2)/(1^3+2^3)+(1+2+3)/(1^3...

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  7. The coefficient of x^(n-2) in the polynomial (x-1)(x-2)(x-3)....(x-n) ...

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  8. The series of natural number is divided into groups as follows , (1), ...

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  9. The sum of 10 terms of the series (x+1/x)^2+(x^2+1/x^2)^2+(x^3+1/x^3)...

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  10. If the sequence 1,2,2,4,4,4,4,,8,8,8,8,8,8,8,8,.... where n consecutiv...

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  11. Sum of n terms of the series (2n-1)+2(2n-3)+3(2n-5)+.... is

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  12. The cubes of the natural numbers are grouped as 1^3,(2^3,3^3),(4^3,5^3...

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  13. Let f(n)=[1/2+n/100] where [x] denote the integral part of x. Then th...

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  14. ABC is a right angled triangle in which angleB=90^@ and BC=a. If n poi...

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  15. If a,b,c are three distinct positive real number such that a^2+b^2+c^2...

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  16. The sum of the series 1^3 - 2^3 + 3^3 - ....+ 9^3=

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  17. If x1, x2 , x3 and y1 , y2 , y3 are both in G.P. with the same common ...

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  18. Let two numbers have arithmetic mean 9 and geometric mean 4. Then thes...

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  19. The sum of the first n terms of the series 1^2+2.2^2+3^2+2.4^2+5^2+2.6...

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  20. Let a1 , a2 , a3,.... be terms of an A.P. if (a1 + a2 +....+ ap)/(a1 +...

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