જો sum_{ r =0}^5 frac{{ }^{11} C _{2 r +1}}{2 | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$\int_0^1(1+x)^{11} d x=\left[C_0 x+\frac{C_1 x^2}{2}+\frac{C_2 x^3}{3}+\ldots\right]_0^1$
$\frac{2^{12}-1}{12}=C_0+\frac{C_1}{2}+\frac{C_2}{3}+\frac

Vedclass · Accepted Answer

$2035$

Vedclass · Answer

$\int_0^1(1+x)^{11} d x=\left[C_0 x+\frac{C_1 x^2}{2}+\frac{C_2 x^3}{3}+\ldots\right]_0^1$
$\frac{2^{12}-1}{12}=C_0+\frac{C_1}{2}+\frac{C_2}{3}+\frac{C_3}{4}+\ldots$
$\int_{-1}^0(1+x)^{11} d x=\left[C_0 x+\frac{C_1 x^2}{2}+\frac{C_2 x^3}{3}+\ldots\right]_{-1}^0$
$\frac{1}{12}=C_0-\frac{C_1}{2}+\frac{C_2}{3}-\frac{C_3}{4}+\ldots$
$\frac{2^{12}-2}{12}=2\left(\frac{C_1}{2}+\frac{C_3}{4}+\frac{C_5}{6}+\ldots\right)$
$\frac{C_1}{2}+\frac{C_3}{4}-\frac{C_5}{6}+\ldots=\frac{2^{11}-1}{12}=\frac{2047}{12}$

જો $\sum_{ r =0}^5 \frac{{ }^{11} C _{2 r +1}}{2 r +2}=\frac{ m }{ n }, \operatorname{gcd}( m , n )=1$,હોય તો $m - n$ ની કિમંત મેળવો.

Similar Questions

${(1 + x - 3{x^2})^{3148}}$ ના સહગુણકનો સરવાળો મેળવો.

$(1+x)^{10}$ ના દ્વિપદી વિસ્તરણમાં $x^{10-r}$ નો સણગુણક જો $a_r$ હોય., તો $\sum \limits_{r=1}^{10} r^3\left(\frac{a_r}{a_{r-1}}\right)^2=...............$

$(1 + t^2)^{25} (1 + t^{25}) (1 + t^{40}) (1 + t^{45}) (1 + t^{47})$ ના વિસ્તરણમાં $t^{50}$ નો સહગુણક મેળવો

જો $n$ એ $1$ કરતાં મોટો પૂર્ણાક હોય , તો $a{ - ^n}{C_1}(a - 1){ + ^n}{C_2}(a - 2) + .... + {( - 1)^n}(a - n) = $