Find (33−23)+(53−43)+(73−63)+.... to 10 terms. Or Show that 1×2

1.	Find (33−23)+(53−43)+(73−63)+.... to 10 terms. Or Show that 1×22+2×32+....+n×(n+1)212×2+22×3+....+n2×(n+1)=3n+53n+1
Answer» Find $(3^{3} - 2^{3}) + (5^{3} - 4^{3}) + (7^{3} - 6^{3}) + . . . .$ to 10 terms. Or Show that $\frac{1 \times 2^{2} + 2 \times 3^{2} + . . . . + n \times (n + 1)^{2}}{1^{2} \times 2 + 2^{2} \times 3 + . . . . + n^{2} \times (n + 1)} = \frac{3 n + 5}{3 n + 1}$

Find (33−23)+(53−43)+(73−63)+.... to 10 terms. Or Show that 1×22+2×32+....+n×(n+1)212×2+22×3+....+n2×(n+1)=3n+53n+1

Answer»

Find $(3^{3} - 2^{3}) + (5^{3} - 4^{3}) + (7^{3} - 6^{3}) + . . . .$ to 10 terms.

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

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Find (33−23)+(53−43)+(73−63)+.... to 10 terms. Or Show that 1×22+2×32+....+n×(n+1)212×2+22×3+....+n2×(n+1)=3n+53n+1

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