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Show that 1^4/13+2^4/3.5+3^4/5.7+.....+n...

Show that `1^4/13+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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Find the sum (1^4)/(1xx3)+(2^4)/(3xx5)+(3^4)/(5xx7)+......+(n^4)/((2n-1)(2n+1))

Prove by mathematical induction that 1/1.3+1/3.5+1/5.7+...+1/((2n-1)(2n+1)) = n/(2n+1),(n in N)

Prove by induction that (1)/(1*3)+(1)/(3*5)+(1)/(5*7)+ . . .+(1)/((2n-1)(2n+1))=(n)/(2n+1)(ninNN) .

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

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 that by using the principle of mathematical induction for all n in N : (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))

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Prove that by using the principle of mathematical induction for all n in N : (1)/(3.5)+ (1)/(5.7)+ (1)/(7.9)+ ....+(1)/((2n+1)(2n+3))= (n)/(3(2n+3))

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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. If (m+1)^th ,(n+1)^th and (r+1)^th terms in AP are in GP m,n,r are in ...

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  2. If p be the first of n arithmetic means between two numbers and q be t...

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  3. Show that 1^4/13+2^4/3.5+3^4/5.7+.....+n^4/((2n-1)(2n+1))=(n(4n^2+6n+5...

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  4. Solve the following equations for x and y log10xx+1/2log10xx+1/4log10x...

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  5. Find the sum of the series 1/1.3+2/(1.3.5)+3/(1.3.5.7)...upto infinit...

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  6. If sum(r=1)^nTr =n/8(n+1)(n+2)(n+3) then find sum(r=1)^n1/Tr

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  7. If 1,log9(3^(1-x)+2) and log3(4.3^x-1) are in AP , then x is equal to

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  8. If the sum of the first 2n terms of the AP 2,5,8.....is equal to the s...

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  9. If xin R , the number 5^(1+x)+5^(1-x),a/2,25^x+25^-xform an AP , then ...

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  10. If an AP a7=9 and a1a2a7 is least , then common difference is

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  11. Consider an infinite geometric series with first term a and common rat...

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  12. The value of a^(logb(x))=(where, a=0.2,b=sqrt5), x=(1/4+1/8+1/16+........

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  13. If a,b,c are in HP and agtcgt0, then 1/(b-c)-1/(a-b).

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  14. Let the positive numbers a,b,c,d be in AP , Then abc, abd,acd,bcd are

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  15. If a,b,c are in HP , thn the value of (b+a)/(b-a)+(b+c)/(b-c) is

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  16. If x1gt0,i=1,2.....50 and x1+x2+.....x50=50 then the minimum value of ...

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  17. If three positive real number a,b,c are in AP with abc =4 , then the m...

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  18. The sum of 10 terms of the series 0.7+.77+.777+.... is

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  19. Find the sum of the series upto n terms 1.3.5+3.5.7+5.7.9+....

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  20. Find the sum of first n terms of the series 3/1^2+5/(1^2+2^2)+7/(1^2+2...

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