Question

find the n number of series: 1x2² + 3 x 3² + 5 x 4²+...+...

Answer 1

Step-by-step explanation:





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Question



Show that 12×2+22×3+...+n2×(n+1)1×22+2×32+...+n×(n+1)2=3n+13n+5

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Solution



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The nth term of the numerator =n(n+1)2=n2+2n2+n

And nth term of the denominator =n2(n+1)=n3+n2

∴12×2+22×3+...+n2×(n+1)1×22+2×32+...+n×(n+1)2=∑