118893 If \(\sum_{k=1}^n k(k+1)(k-1)=\mathbf{p n}^4+\mathbf{q} \mathbf{n}^3+\mathbf{t n}^2+\mathbf{s n}\), where \(p, q, t\) and \(s\) are constants, then the value of \(s\) is equal to

118894 Let \(S_1, S_2, \ldots S_n\) be squares such that for each \(n\) \(\geq 1\), the length of a side of \(S_n\) equals the length of the diagonal of \(S_{n+1}\). If the length of a side of \(S_1\) is \(10 \mathrm{~cm}\), then the least value of \(n\) for which the area of \(S_n\) less than \(1 \mathrm{sq} \mathbf{~ c m}\)

118895 The value of \(4+2(1+2) \log 2+\) \(\frac{2\left(1+2^2\right)}{2 !}(\log 2)^2+\frac{2\left(1+2^3\right)}{3 !}(\log 2)^3+\ldots .\). is

118896 The value of \(\log \left(10+10 x+10 x^2+\ldots \ldots.\right)\) is

118893 If \(\sum_{k=1}^n k(k+1)(k-1)=\mathbf{p n}^4+\mathbf{q} \mathbf{n}^3+\mathbf{t n}^2+\mathbf{s n}\), where \(p, q, t\) and \(s\) are constants, then the value of \(s\) is equal to

118894 Let \(S_1, S_2, \ldots S_n\) be squares such that for each \(n\) \(\geq 1\), the length of a side of \(S_n\) equals the length of the diagonal of \(S_{n+1}\). If the length of a side of \(S_1\) is \(10 \mathrm{~cm}\), then the least value of \(n\) for which the area of \(S_n\) less than \(1 \mathrm{sq} \mathbf{~ c m}\)

118895 The value of \(4+2(1+2) \log 2+\) \(\frac{2\left(1+2^2\right)}{2 !}(\log 2)^2+\frac{2\left(1+2^3\right)}{3 !}(\log 2)^3+\ldots .\). is

118896 The value of \(\log \left(10+10 x+10 x^2+\ldots \ldots.\right)\) is

118893 If \(\sum_{k=1}^n k(k+1)(k-1)=\mathbf{p n}^4+\mathbf{q} \mathbf{n}^3+\mathbf{t n}^2+\mathbf{s n}\), where \(p, q, t\) and \(s\) are constants, then the value of \(s\) is equal to

118894 Let \(S_1, S_2, \ldots S_n\) be squares such that for each \(n\) \(\geq 1\), the length of a side of \(S_n\) equals the length of the diagonal of \(S_{n+1}\). If the length of a side of \(S_1\) is \(10 \mathrm{~cm}\), then the least value of \(n\) for which the area of \(S_n\) less than \(1 \mathrm{sq} \mathbf{~ c m}\)

118895 The value of \(4+2(1+2) \log 2+\) \(\frac{2\left(1+2^2\right)}{2 !}(\log 2)^2+\frac{2\left(1+2^3\right)}{3 !}(\log 2)^3+\ldots .\). is

118896 The value of \(\log \left(10+10 x+10 x^2+\ldots \ldots.\right)\) is

118893 If \(\sum_{k=1}^n k(k+1)(k-1)=\mathbf{p n}^4+\mathbf{q} \mathbf{n}^3+\mathbf{t n}^2+\mathbf{s n}\), where \(p, q, t\) and \(s\) are constants, then the value of \(s\) is equal to

118894 Let \(S_1, S_2, \ldots S_n\) be squares such that for each \(n\) \(\geq 1\), the length of a side of \(S_n\) equals the length of the diagonal of \(S_{n+1}\). If the length of a side of \(S_1\) is \(10 \mathrm{~cm}\), then the least value of \(n\) for which the area of \(S_n\) less than \(1 \mathrm{sq} \mathbf{~ c m}\)

118895 The value of \(4+2(1+2) \log 2+\) \(\frac{2\left(1+2^2\right)}{2 !}(\log 2)^2+\frac{2\left(1+2^3\right)}{3 !}(\log 2)^3+\ldots .\). is

118896 The value of \(\log \left(10+10 x+10 x^2+\ldots \ldots.\right)\) is