Exponential and Logarithmic Series

JEE Main Mathematics · Progressions · 6 questions, latest first

• The value of Σ_k=1^∞(-1)^k+1((k(k+1))/(k!)) is202628 January, Shift 1 · Q15
• The sum 1+(1+3)/(2!)+(1+3+5)/(3!)+(1+3+5+7)/(4!)+… upto ∞ terms, is equal to20253 April, Shift 2 · Q6
• If 1+(√3-√2)/(2 √3)+(5-2 √6)/18+(9 √3-11 √2)/(36 √3)+(49-20 √6)/180+… upto ∞=2+(√(b/a)+1) log_e(a/b), where a and b are integers…20245 April, Shift 2 · Q22
• Let a=1+(^2 C_2)/(3!)+(^3 C_2)/(4!)+(^4 C_2)/(5!)+…; b=1+(^1 C_0+^1 C_1)/(1!)+(^2 C_0+^2 C_1+^2 C_2)/(2!)+(^3 C_0+^3 C_1+^3…20244 April, Shift 1 · Q23
• The sum Σ_n=1^∞ (2 n^2+3 n+4)/((2 n)!) is equal to:20231 February, Shift 2 · Q67
• Let Σ_n=0^∞ (n^3((2 n)!)+(2 n-1)(n!))/((n!)((2 n)!))=ae+b/e+c, where a, b, c ∈ Z and e=Σ_n=0^∞ 1/(n!) Then a^2-b+c is equal to…202330 January, Shift 1 · Q81