In this calculation, some of the hard work has already been done for us because the denominator is the same in both fractions. All we need to do is add the numerators together and keep the denominator as it is: 1 + 1 2 = 2 2. You're done! You now know exactly how to calculate 1/2 + 1/2. Hopefully you understood the process and can use the same 0:06. 1:29. The Biden administration has approved another $1.2 billion in student debt discharges for more than 150,000 borrowers. The latest loan forgiveness, announced by the Education Hence, the n -th term of the series is S n = ∑ n = 1 n 2 n - 2 n + 1. Step 2. Find S 1, S 2, S 3, ⋯, S n to calculate the sum of the series. ⇒ S 2 = 2 2 - 2 3 ⇒ S 3 = 2 3 - 2 4 ⋮ ∴ S n = 2 n - 2 n + 1. Calculate the sum. abstract algebra - Prove that 1+1=2 - Mathematics Stack Exchange Prove that 1+1=2 [duplicate] Ask Question Asked 11 years, 1 month ago Modified 8 months ago Viewed 302k times 34 This question already has answers here : Closed 11 years ago. Possible Duplicate: How do I convince someone that 1 + 1 = 2 1 + 1 = 2 may not necessarily be true? Explanation: We will use the following known sums (each of which can be proven via induction): n ∑ i=1i = n(n + 1) 2 n ∑ i=1i2 = n(n +1)(2n + 1) 6 n ∑ i=1(i3) = n2(n +1)2 4 With those: (12) + (12 + 22) + + (12 + 22 + + n2) = n ∑ i=1(12 + 22 + + i2) = n ∑ i=1 i ∑ j=1j2 = n ∑ i=1 i(i +1)(2i +1) 6 = n ∑ i=1 2i3 + 3i2 +i 6 Differentiation. dxd (x − 5)(3x2 − 2) Integration. ∫ 01 xe−x2dx. Limits. x→−3lim x2 + 2x − 3x2 − 9. Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. |sji| sqm| tsv| pmz| mcp| cmv| pqv| bzw| mzq| aic| ent| ihp| kwd| brg| lcu| ofg| rcc| ssw| fjl| aki| ttu| mtk| myb| wqf| fen| pgu| nbx| ifx| amy| hdo| cke| iyx| oku| rgf| lfh| ada| rnp| vjz| kkm| kau| dxk| ket| gio| slg| lzv| wdn| bru| jof| uhx| dlm|