Find the 24th term in the expansion of $(a+b)^25$ ?

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Answer 1 · 2018-03-27T16:50:28

$t_24=-300 *a^2 *b^23$

We know that , in the expansion of $(a+b)^n$

$T_(r+1)=(-1)^rC_r^n(a)^(n-r)(b)^r$

Comparing $(a+b)^25 with, (a+b)^n$

$n=25 and r+1=24=>r=23$

So,

$T_(23+1)=(-1)^23 C_23^25 (a)^(25-23)(b)^23....to(I)$

Now , $(-1)^23=-1$

and $C_r^n=C_(n-r)^n$

$=>C_23^25= C_(25-23)^25=C_2^25=(25xx24)/(2xx1)=300$

Hence, from $(I)$

$t_24=-300 *a^2 *b^23$

Find the 24th term in the expansion of (a+b)^25(a+b)^25?