Question

9) If
If 1×2 + 2×3 +3×4 + 4×5 +......upto n terms ÷ 1+2+3+4+.....upto n terms =100/3

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Answer 1

Answer:

iska answer hai 1920 hai it is right answer

Answer 2

Answer:

first we take up the series

S1 = 1x2+2x3+3x4+....upto n terms

the pth term of the series would be

pth term = px(p+1)

= p^2 + p

now summing this from p = 1 to n we have

S1 = sigma(1 to n) (p^2 + p)=

= sigma( to n) p^2 + sigma(1to n) p

= n(n+1)(2n+1)/6 + n(n+1)/2

= n(n+1)/6 {2n+1 +3}

= n(n+1)(2n+4)/6

S1 = n(n+1)(n+2)/3

second series

S2 = 1+2+3+4+...n terms

= n(n+1)/2

now S1/S2 = 100/3

{n(n+1)(n+2)/3} / n(n+1)/2 = 100/3

2(n+2)/3 = 100/3

n+2 = 50

n = 48