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Question: If (1 + x) (1+ x + x2)(1 + x + x2 + x3).......... (1 + x + x2 + x3 +...+ xn) = a0 + a1x + a2x2 + .....

If (1 + x) (1+ x + x2)(1 + x + x2 + x3)..........

(1 + x + x2 + x3 +...+ xn) = a0 + a1x + a2x2 + ....+ amxm then ∑r=0mar=\sum_{r = 0}^{m}{a_{r} =}

A

1

B

n

C

n + 1!

D

n!

Answer

n!

Explanation

Solution

(1 + x) (1 + x + x2) (1+ x + x2 + x3) ....(1 + x + x2 +....xn)

= a0 + a1x + a2x2 +.....+amxm

substituting x = 1

1 × (2) (3) (4)........ (n) = ∑r=0mar=\sum_{r = 0}^{m}{a_{r} =} n!