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Question

Find the sum upto n terms
11.2.3+12.3.4+13.4.5+.....

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Solution

nx=11x(x+1)(x+2)=nx=1(x+2)2(x+1)+xx(x+1)(x+2)
nx=11x(x+1)nx=122(x+2)+nx=11(x+1)(x+2)
=nx=1(x+1)xx(x+1)nx=1(x+2)xx(x+2)+nx=1(x+2)(x+1)(x+1)(x+2)
=nx=11x1x+1nx=11x1x+2+nx=11x+11x+2
=nx=11x1x+1nx=1[(121x+1)+(1x+11x+2)]+nx=11x+11x+2
(11n+1)(11n+1+121n+2)+(121n+2)
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1067798_1165412_ans_f5bcbe6e545342c797250bee879cceb4.png

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