If |x| lt 1 then 1+n ((2x)/(1+x))+(n(n+1...

If `|x| lt 1` then `1+n ((2x)/(1+x))+(n(n+1))/(2!) ((2x)/(1=x))^2 + ….....oo=`

`((2x)/(1+x))^(n)`

`((1+x)/(2x))^(n)`

`((1-x)/(1+x))^(n)`

`((1+x)/(1-x))^(n)`

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If |x|<1 then 1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^(2)+......oo

|x|<1, then 1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^(2)+ is equal to a.((2x)/(1+x))^(n) b.((1+x)/(2x))^(n) c.((1-x)/(1+x))^(n) d.((1+x)/(1-x))^(n)

If |x|lt(1)/(2), what is the value of 1+[(x)/(1-x)]+[(n(n+1))/(2!)][(x)/(1-x)]^(2)+............+oo ?

Let n is a rational number and x is a real number such that |x|lt1, then (1+x)^(n)=1+nx+(n(n-1)x^(2))/(2!)+(n(n-1)(n-2))/(3!).x^(3)+ . . . This can be used to find the sum of different series. Q. Sum of infinite series 1+(2)/(3)*(1)/(2)+(2)/(3)*(5)/(6)*(1)/(2^(2))+(2)/(3)*(5)/(6)*(8)/(9)*(1)/(2^(3))+ . . .oo is

The sum of 1+n(1-(1)/(x))+(n(n+1))/(2!)(1-(1)/(x))^(2)+...oo will be x^(n) b.x^(-n) c.(1-(1)/(x))^(n) d.none of these

If x+1/x=-2 then x^(2n+1)+1/(x)^(2n+1)=

lim_ (x rarr oo x rarr oo) ((1 ^ ((1) / (x)) + 2 ^ ((1) / (x)) + 3 ^ ((1) / (x)) + ... + n ^ ((1) / (x))) / (n)) ^ (nx) is

If |x|<1 , then lim_(n rarr oo)(1+x)(1+x^(2))(1+x^(4))...(1+x^(2^n))=

lim_ (n rarr oo) (1) / (2) tan ((x) / (2)) + (1) / (2 ^ (2)) tan ((x) / (2 ^ (2))). ... + (1) / (2 ^ (n)) tan ((x) / (2 ^ (n))) is equal to lim_ (n rarr oo) sum_ (n = 1) ^ (n) (1 ) / (2 ^ (n)) tan ((x) / (2 ^ (n)))

DISHA PUBLICATION-BINOMIAL THEOREM -EXERCISE-1 (CONCEPT BUILDER )

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