︠7fada08f-b879-453b-96f7-916d0505d4bbs︠
N(ln(7))
var('k')
sum (1/k,k,3,8)
N(sum(1/k,k,3,8))
︡f1e1bc46-f0c3-476e-93f3-9df9addd32ba︡{"stdout":"1.94591014905531"}︡{"stdout":"\n"}︡{"stdout":"k\n"}︡{"stdout":"341/280"}︡{"stdout":"\n"}︡{"stdout":"1.21785714285714\n"}︡{"done":true}
︠b90dde32-b7fe-4b44-b1bf-92bb9df7b09bs︠
var('s')
sum(1/(s+1),s,1,6)
︡d274c3d9-0149-430d-82f1-45f0942390a2︡{"stdout":"s\n"}︡{"stdout":"223/140\n"}︡{"done":true}
︠78df1740-213b-4f77-93da-27aa614f388bs︠
var('z')
sum((1/2)*(2/(z+2)),z,1,12)
︡f2cf57b9-8863-4276-bc05-b5c1a00d070f︡{"stdout":"z\n"}︡{"stdout":"631193/360360\n"}︡{"done":true}
︠2ea8be17-c56a-4321-b76a-2db36f01898bs︠
k = 0
var('j')
numerical_approx(sum(1/(j+2^k),j,2,7))
numerical_approx(ln(7)-sum(1/(j+2^k),j,2,7))
︡88ff3bd0-2cb0-4ae1-82d9-c01e2e760a1e︡{"stdout":"j\n"}︡{"stdout":"1.21785714285714\n"}︡{"stdout":"0.728053006198170\n"}︡{"done":true}
︠404b8560-567d-4851-895e-cf0b5e278140s︠
k = 1
var('j')
numerical_approx(sum(1/(j+2^k),j,2,13))
numerical_approx(ln(7)-sum(1/(j+2^k),j,2,13))
︡a38692c4-2e7e-4647-a210-56450113df21︡{"stdout":"j\n"}︡{"stdout":"1.48489565989566\n"}︡{"stdout":"0.461014489159653\n"}︡{"done":true}
︠3188ce2f-800f-471f-bf78-e68c95a0dbf3s︠
k = 2
var('j')
numerical_approx(sum(1/(j+2^k),j,2,25))
numerical_approx(ln(7)-sum(1/(j+2^k),j,2,25))
︡161cff22-b299-42cc-ac97-f7d582da3ad3︡{"stdout":"j\n"}︡{"stdout":"1.67832046425372\n"}︡{"stdout":"0.267589684801589\n"}︡{"done":true}
︠697bdb18-d4bd-477b-aa70-d02d0d49e775s︠
k = 3
var('j')
numerical_approx(sum(1/(j+2^k),j,2,49))
numerical_approx(ln(7)-sum(1/(j+2^k),j,2,49))
︡364368fa-5ea8-4f71-91b6-bbddddbc302e︡{"stdout":"j\n"}︡{"stdout":"1.80004496046410\n"}︡{"stdout":"0.145865188591214\n"}︡{"done":true}
︠ea4b5f12-ac46-4b07-bd5c-021bdd38a144s︠
k = 4
var('j')
numerical_approx(sum(1/(j+2^k),j,2,97))
numerical_approx(ln(7)-sum(1/(j+2^k),j,2,97))
︡5eee9297-b1e1-4866-80b0-c1a153bf779a︡{"stdout":"j\n"}︡{"stdout":"1.86946921356292\n"}︡{"stdout":"0.0764409354923892\n"}︡{"done":true}
︠2231a0a8-7ac4-40ac-97d1-61a4c28cba62s︠
k = 5
var('j')
numerical_approx(sum(1/(j+2^k),j,2,193))
numerical_approx(ln(7)-sum(1/(j+2^k),j,2,193))
︡a8474a4d-5110-4539-9ec8-8f756b8faecc︡{"stdout":"j\n"}︡{"stdout":"1.90673841750134\n"}︡{"stdout":"0.0391717315539719\n"}︡{"done":true}
︠b9f11fc7-80d9-4bbb-9f17-d7882553be4bs︠
k = 6
var('j')
numerical_approx(sum(1/(j+2^k),j,2,385))
numerical_approx(ln(7)-sum(1/(j+2^k),j,2,385))
︡77ef7e74-4aad-4ed3-9232-7cc8729cab9a︡{"stdout":"j\n"}︡{"stdout":"1.92607620594197\n"}︡{"stdout":"0.0198339431133410\n"}︡{"done":true}
︠38a9e784-baee-4759-bd8d-56a78bc0cf68s︠
k = 7
var('j')
numerical_approx(sum(1/(j+2^k),j,2,769))
numerical_approx(ln(7)-sum(1/(j+2^k),j,2,769))
︡df8a48b4-18f2-45ee-beeb-84ce8cd5bcc1︡{"stdout":"j\n"}︡{"stdout":"1.93592980641759\n"}︡{"stdout":"0.00998034263772207\n"}︡{"done":true}
︠e1717c9e-6ebf-4930-a9a5-bf12b100add5s︠
k = 8
var('j')
numerical_approx(sum(1/(j+2^k),j,2,1537))
numerical_approx(ln(7)-sum(1/(j+2^k),j,2,1537))
︡16738a8b-45ba-438d-b3fe-047726626ed7︡{"stdout":"j\n"}︡{"stdout":"1.94090396142640\n"}︡{"stdout":"0.00500618762891558\n"}︡{"done":true}