a=2,b=3a=2, b=3a=2,b=3 এবং c=5c=5c=5
ক) দেখাও যে, 3n−1(3)n+1=(3)n−1\frac{3^{n}-1}{(\sqrt{3})^{n}+1}=(\sqrt{3})^{n}-1(3)n+13n−1=(3)n−1।
খ) সরল কর: an+1⋅b2n−m⋅cm+n⋅(ab)m(ab)n⋅(ac)m+2⋅(bc)n÷(52)−1\frac{a^{n+1} \cdot b^{2 n-m} \cdot c^{m+n} \cdot(a b)^{m}}{(a b)^{n} \cdot(a c)^{m+2} \cdot(b c)^{n}} \div\left(5^{2}\right)^{-1}(ab)n⋅(ac)m+2⋅(bc)nan+1⋅b2n−m⋅cm+n⋅(ab)m÷(52)−1।
দেখাও যে, 3n−1(3)n+1=(3)n−1\frac{3^{n}-1}{(\sqrt{3})^{n}+1}=(\sqrt{3})^{n}-1(3)n+13n−1=(3)n−1।
সরল কর: an+1⋅b2n−m⋅cm+n⋅(ab)m(ab)n⋅(ac)m+2⋅(bc)n÷(52)−1\frac{a^{n+1} \cdot b^{2 n-m} \cdot c^{m+n} \cdot(a b)^{m}}{(a b)^{n} \cdot(a c)^{m+2} \cdot(b c)^{n}} \div\left(5^{2}\right)^{-1}(ab)n⋅(ac)m+2⋅(bc)nan+1⋅b2n−m⋅cm+n⋅(ab)m÷(52)−1।
