Show that 1×22+2×32+……+n×(n+1)212×2+22×3+……+n2×(n+1)=3n+

1.	Show that 1×22+2×32+……+n×(n+1)212×2+22×3+……+n2×(n+1)=3n+53n+1
Answer» Show that $\frac{1 \times 2^{2} + 2 \times 3^{2} + \dots \dots + n \times (n + 1)^{2}}{1^{2} \times 2 + 2^{2} \times 3 + \dots \dots + n^{2} \times (n + 1)} = \frac{3 n + 5}{3 n + 1}$

Show that 1×22+2×32+……+n×(n+1)212×2+22×3+……+n2×(n+1)=3n+53n+1

Answer»

Show that

$\frac{1 \times 2^{2} + 2 \times 3^{2} + \dots \dots + n \times (n + 1)^{2}}{1^{2} \times 2 + 2^{2} \times 3 + \dots \dots + n^{2} \times (n + 1)} = \frac{3 n + 5}{3 n + 1}$

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Show that 1×22+2×32+……+n×(n+1)212×2+22×3+……+n2×(n+1)=3n+53n+1

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