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Sum of the series a^n+a^(n-1)b+^(n-2)b^2...

Sum of the series `a^n+a^(n-1)b+^(n-2)b^2+………..+ab^n` can be obtained by taking outt `a^n or b^n` comon and using the forumula of sum of `(n+1)` terms of G.P. N the basis of above information answer the following question:Um of coeficients of `x^50` and `x^51` in `(1+x)^199+(1+x)^198x+(1+x)6197x^2+..+(1+x)x^198+x^199` is euqla to the coefficient of `x^r in `(1+x)^200+(1+x)^199x+(1+x0^198x^2+.........+(1+x)x^199+x^200` then r may be equal to (A) 51 (B) 52 (C) 53 (D) none of these

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Sum of the series a^n+a^(n-1)b+^(n-2)b^2+………..+ab^n can be obtained by taking outt a^n or b^n comon and using the forumula of sum of (n+1) terms of G.P. N the basis of above information answer the following question: Coefficient of x^50 in (1+x)^1000+x(1+x)^999+........+x^999(1+x)+x^1000 is (A) ^1000C_50 (B) ^1002C_50 (C) ^1001C_50 (D) ^1001C_49

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