Question

if 1×3+2×5+3×7+.....upto n terms/1³+2³+3³+..... upto n terms = 5/9 find the value of n

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Answer 1

Answer:

Step-by-step explanation:

On solving numerator = ∑n(n + 2)

=> ∑( $n^{2} + 2n$ )       → n(n +1)(2n +1)/6 + n(n+1)

                             → n(n +1)[ (2n + 1)/6 + 1 ]

On solving the denominator = $[n(n +1)]^{2} / 4$

On combining numerator and denominator,

→ (2n + 7)/6 ÷ n(n +1)/4 = 5/9

→ (2n + 7)/ [n(n + 1)] = 5/6

→ $5n^{2} - 7n - 42 = 0$

 

I HOPE THE REST YOU CAN EASILY SOLVE...