Among the following four statements,the state | vedclass

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(C) We check each statement for $n = 1$: $(A)$ $(2(1) + 7)  \frac{1^3}{3} \implies 1 > \frac{1

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$3 \cdot 5^{2n + 1} + 2^{3n + 1}$ is divisible by $23$

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(C) We check each statement for $n = 1$: $(A)$ $(2(1) + 7) $(B)$ $1^2 > \frac{1^3}{3} \implies 1 > \frac{1}{3}$,which is True. $(C)$ For $n = 1$,$3 \cdot 5^{2(1) + 1} + 2^{3(1) + 1} = 3 \cdot 5^3 + 2^4 = 3 \cdot 125 + 16 = 375 + 16 = 391$. Checking divisibility: $391 \div 23 = 17$. Since $391$ is divisible by $23$,this statement is True for $n=1$. Wait,let us re-check $n=2$ for $(C)$: $3 \cdot 5^5 + 2^7 = 3 \cdot 3125 + 128 = 9375 + 128 = 9503$. $9503 \div 23 = 413.17$. Thus,it is not divisible by $23$ for all $n$. $(D)$ For $n = 1$,$2 = \frac{1(5(1) - 1)}{2} = \frac{4}{2} = 2$,which is True. Therefore,the statement that is not true for all $n \in N$ is $(C)$.

Among the following four statements,the statement which is not true for all $n \in N$ is

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