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  4. If S =1.2(22-12)+2.3(32-22)+3.4(42-32) + .... upto 50 terms, then S is

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Q. If $S =1.2\left(2^{2}-1^{2}\right)+2.3\left(3^{2}-2^{2}\right)+3.4\left(4^{2}-3^{2}\right)$ + .... upto $50$ terms, then S is

Sequences and Series

Solution:

$T _{ r }= r ( r +1)\left[( r +1)^{2}- r ^{2}\right]$