Suppose for each n∈N,14+24+34+…+n4=an5+bn4+cn3+dn2+en+f, then value of b is

# Suppose for each $n\in \mathbf{N},{1}^{4}+{2}^{4}+{3}^{4}+\dots +{n}^{4}=a{n}^{5}+b{n}^{4}+c{n}^{3}+d{n}^{2}+en+f$, then value of $b$ is

1. A

$1/5$

2. B

$1/2$

3. C

$1/3$

4. D

1

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### Solution:

We have

and ${1}^{4}+{2}^{4}+\dots +{n}^{4}+\left(n+1{\right)}^{4}$

Subtracting $\left(1\right)$ from $\left(2\right)$, we get

Comparing coefficients fo ${n}^{4}$ , we get

Comparing coefficient fo ${n}^{3}$ , we get

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