JEE Main202324 Jan 2023Evening ShiftMathematicsSequences and SeriesActual
If 1 3 + 2 3 + 3 3 . . . . . . upto n terms 1 · 3 + 2 · 5 + 3 · 7 + . . . . upto n terms = 9 5 then the value of n is
Correct answer
0
Step-by-step solution
Given, 1 3 + 2 3 + 3 3 . . . . . . . n 3 1 · 3 + 2 · 5 + 3 · 7 + . . . . n 2 n + 1 = 9 5 Now we know that 1 3 + 2 3 + 3 3 . . . . . . . n 3 = n n + 1 2 2 And Σ n 2 n + 1 = 2 Σ n 2 + Σ n ⇒ Σ n 2 n + 1 = 2 × n n + 1 2 n + 1 6 + n n + 1 2 ⇒ Σ n 2 n + 1 = n n + 1 2 n + 1 3 + n n + 1 2 So putting the value in the given equation we get, 1 3 + 2 3 + 3 3 . . . . . . . n 3 1 · 3 + 2 · 5 + 3 · 7 + . . . . n 2 n + 1 = 9 5 ⇒ n n + 1 2 2 n n + 1 2 n +