Show that12+2+22×3+...n2(n+1)1×22+2×32+...+n(n+1)2 =3n+13n+5

=3n2+7n+23n2+11n+10 =(3n+1)(n+2)(3n+5)(n+2)=3n+13n+5 = RHS

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Show that {1 2^{2} + 2 3^{2} + ... + n(n + 1)^{2}}{1^{2} + 2

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

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Show that

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

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= \frac{3 n ^{2} + 11 n + 10}{3 n ^{2} + 7 n + 2} = \frac{( 3 n + 5 ) ( n + 2 )}{( 3 n + 1 ) ( n + 2 )}

= \frac{3 n + 5}{3 n + 1}

= RHS

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Question Text	Show that $\frac{1 \times 2 ^{2} + 2 \times 3 ^{2} + ... + n ( n + 1 ) ^{2}}{1 ^{2} + 2 + 2 ^{2} \times 3 + ... n ^{2} ( n + 1 )} = \frac{3 n + 5}{3 n + 1}$
Answer Type	Text solution:1
Upvotes	150