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1.2+2.3+3.4+…………..+n(n+1)=n/3(n+1)(n+2) ...

`1.2+2.3+3.4+…………..+n(n+1)=n/3(n+1)(n+2) forall n in N.`

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1/1.2+1/2.3+1/3.4+…………….+1/(n(n+1))=n/(n+1) forall n in N.

1*2*3+2*3*4+...+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4 forall n in N.

1^(3)+2^(3)+3^(3)+………….+n^(3)=(n^(2)(n+1)^(2))/4 forall n in N.

1/1.4+1/4.7+1/7.10+...+1/((3n-2)(3n+1))=n/((3n+1)) forall n in N.

1+2+3+............+n=(n(n+1))/2 forall n in N.

1^(2)+2^(2)+3^(2)+............+n^(2)=(n(n+1)(2n+1))/6 forall n in N.

1/(2*5)+1/(5*8)+1/(8*11)+............1/((3n-1)(3n+2))=n/((6n+4)) forall n in N.

(1+3/1)(1+5/4)(1+7/9)...(1+((2n+1))/n^(2))=(n+1)^(2) forall n in N.

Prove that by using the principle of mathematical induction for all n in N : 1.2.3+ 2.3.4+ ....+ n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/(4)

Prove that by using the principle of mathematical induction for all n in N : 1.2+ 2.3+ 3.4+ .....+n(n+1)= [(n(n+1)(n+2))/(3)]

OSWAAL PUBLICATION-SAMPLE PAPER 6-EXERCISE
  1. In how many of distinct permutations of the letters in the word MISSIS...

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  2. (iii) Find the modulus and argument of the complex numbers. (a) (1+i...

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  3. A and B are two events such that P(A) =0.54,P(B) =0.69 and P( A nnB) ...

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  4. A and B are two events such that P(A) =0.54,P(B) =0.69 and P( A nnB) ...

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  5. A and B are two events such that P(A) =0.54,P(B) =0.69 and P( A nnB) ...

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  6. Find the derivative of function cot x with respect to x from first pri...

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  7. If a,b,c are in G.P and a^((1)/(x))=b^((1)/(y))=c^((1)/(z)), prove tha...

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  8. Define rational function.If function from f:R-{0} rarr R is defined as...

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  9. Calculate the mean deviation about median for the following distributi...

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  10. cos^(2)A+cos^(2)B-cos^(2)C=1-2sinA sinB cosC

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  11. An examination paper consists of 12 questions diyided in to part A and...

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  12. An examination paper consists of 12 questions diyided in to part A and...

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  13. 1.2+2.3+3.4+…………..+n(n+1)=n/3(n+1)(n+2) forall n in N.

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  14. The second ,third and fourth terms in the binomial expansion (x+a)^n a...

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  15. Derive an expression for the distance between two parallel lines y=mx+...

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  16. Solve the following system of inequalities graphically x+2yle8,2x+yle8...

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  17. prove that cos(A+B)=cosAcosB-sinAsinB

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  18. Find the sum to 'n' terms of 3.1^(2)+5.2^(2)+7.3^(2)+........

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  19. (a)Define a parabola and derive its equation in the standard form y^2=...

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  20. Find derivative:x^2 cos(pi/4)/sin x w.r.t.'x'.

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