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If `(1+x)^n = underset(r=0) ^n n overset sum Crx^r` then prove that `C_1+2C_2+3C_3+…..nC_n=n2^(n-1)`

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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
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  2. Show that if the greatest term in the expansion of (1+x)^(2n) has also...

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  3. If (1+x)^n = underset(r=0) ^n n overset sum Crx^r then prove that C1+...

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  4. If (1+x)^n= underset(r=0)oversetn Crx6r then prove that C0+2.C1+3.C2+…...

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  5. (1+x)^n=^nC0+^nC1x+^nC2x^2+……….+^nCnx^n then find the value of ^nC1+(2...

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  6. (1+x)^n=^nC0+^nC1x+^nC2x^2+……….+^nCnx^n then find the value of ^nC0 + ...

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  7. If (1+x)^n = ^nC0+ ^nC1x+…….+^nCnx^n then find the value of ^nC0//1+^n...

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  8. If (1+x)^n = ^nC0+ ^nC1x+…….+^nCnx^n then find ^nC0//2+^nC1//3+^nC2//4...

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  9. If (1+x)^n = ^nC0+ ^nC1x+…….+^nCnx^n then find ^nC0 ^nCr +^nC1 ^nC(r-1...

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  10. If (1+x)^n = ^nC0+ ^nC1x+…….+^nCnx^n then find ^nC0 ^2+ ^nC1 ^2 +^nC2^...

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  11. If (1+x)^n = ^nC0+ ^nC1x+…….+^nCnx^n then find the value of ^nC1 ^2+2^...

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  12. Let R=(5 sqrt 5+11)^(2n+1) and f=R-[R] where [] is the greatest intege...

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  13. Last three digit of 27^(27)

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  14. Find remainder when 7^(103) is divided by 25.

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  15. If n in I^+ show 2^(3n+3) -7n -8 is divisible by 49.

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  16. Find the coefficient of x^7 in (1+3x-2x^3)^10

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  17. Find the coefficient of a^3b^4c^5 in (ab+bc+ca)^6

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  18. Expand (x^2+(3/x))^4 , xne0

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  19. Compute (98)^5

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  20. Using binomial theorem prove that 6^n-5n always leaves remainder I whe...

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