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(1^4)/1.3+(2^4)/3.5+(3^4)/5.7+......+n^4...

`(1^4)/1.3+(2^4)/3.5+(3^4)/5.7+......+n^4/((2n-1)(2n+1))=(n(4n^2+6n+5))/48+n/(16(2n+1)`

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(1^(2))/(1.3)+(2^(2))/(3.5)+(3^(2))/(5.7)+.....+(n^(2))/ ((2n-1)(2n+1))=((n)(n+1))/((2(2n+1)))

Statement -1: (1^(2))/(1.3)+(2^(2))/(3.5)+(3^(2))/(5.7)+ . . . .+(n^(2))/((2n-1)(2n+1))=(n(n+1))/(2(2n+1)) Statement -2: (1)/(1.3)+(1)/(3.5)+(1)/(5.7)+ . . . .+(1)/((2n-1)(2n+1))=(1)/(2n+1)

1.3+3.5+5.7+......+(2n-1)(2n+1)=(n(4n^(2)+6n-1))/(3)

Find the sum (1^(4))/(1xx3)+(2^(4))/(3xx5)+(3^(4))/(5xx7)+......+(n^(4))/((2n-1)(2n+1))

1.4+2.5+.......+n(n+3)=

Using the principle of mathematical induction prove that (1)/(1.2.3)+(1)/(2.3.4)+(1)/(3.4.5)+...+(1)/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2) for all n in N

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(1.2.3)+(1)/(2.3.4)+(1)/(3.4.5)+...+(1)/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2))

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(2.5)+(1)/(5.8)+(1)/(8.11)+...+(1)/((3n-1)(3n+2))=(n)/((6n+4))=(n)/((6n+4))

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

1.2.3+2.3.4++n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/(4)

RESONANCE DPP-JEE MAINS-All Questions
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  3. (1^4)/1.3+(2^4)/3.5+(3^4)/5.7+......+n^4/((2n-1)(2n+1))=(n(4n^2+6n+5))...

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  4. Let C be a curve passing through M(2,2) such that the slope of the tan...

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  16. sinx+cosx=y^2-y+a has no value of x for any value of y if a belongs to...

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  18. The number of values of a for which equations x^3+a x+1=0a n dx 64+a x...

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  19. Let f(x)=ax^(2)+bx+c, g(x)=ax^(2)+px+q, where a, b, c, q, p in R and b...

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  20. If y=x+e^x , find (d^2x)/(dy^2) .

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