Please explain....

Can neone pls explain how

n{1+(n-1)+(n-1)(n-2)1.2+...........+1}
=n.2^n-1 ?

AND

nx{1+(n-1)x+(n-1)(n-2)1.2x²+........+x^n-1}
=nx(1+x)^n-1 ?

Pleaaaaaaaase do explain this...

2 Answers

the first 1 is ...

nC1 + 2nC2 + 3nC3 ................!!!

now we know ..

(1+x)^n = nC0 + nC1x^1 + .......................

d(1+x)^n/dx = 1nC1 + 2xnC2 +......................

n(1+x)^n-1 = the shit ....

put x = 1...

n2^n-1 = the stuff!!!!!!!

now that u know the first 1 ... the second 1 u just integrate instead of differentiating .... try it ............

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