Isaiah 40:2

דַּבְּרוּ עַל־לֵב יְרוּשָׁלִַם וְקִרְאוּ אֵלֶיהָ כִּי מָלְאָה צְבָאָהּ כִּי נִרְצָה עֲו‍ֹנָהּ כִּי לָקְחָה מִיַּד יְהוָה כִּפְלַיִם בְּכָל־חַטֹּאתֶיהָ׃

2 Speak upon the heart to Jerusalem, and call to her, that her service is finished because her sin is atoned for. For she has received from the hand of the LORD a double amount for all her sins.

דַּבְּרוּ Speak, piel imperative 2 sg, normally found in the piel (Isaiah 8:10; 59:3).

עַל-לֵב יְרוּשָׁלִַם upon the heart to Jerusalem, In Isaiah as in the rest of the Old Testament, the particles עַל,אֶל and לְ are often interchanged. The dual form "Jerusalem" (note the -ayim ending) did not get brought into Greek translations or other writings, Septuagint or otherwise, until well into Christian times.

וְקִרְאוּ אֵלֶיהָ כִּי מָלְאָה צְבָאָהּ  and call to her, that her service is finished. "Service" is most often military, as in the work of being in the army (e.g. Jer. 51:3) although here it could simply refer to hard work of any kind. It can stand for either an army ("the military") or its labor ("the service"). This word, צְבָאָהּ, is marked with a ב in the margin's Mp note because the form occurs on here and in Jeremiah 51:3 (which has the same Mp note).

The verb מָלְאָה is a qal perfect meaning "full, finished," the passive επλησθη "filled up" in the Greek of the LXX.  The כִּי here merely expresses the content of the "call.

כִּי נִרְצָה עֲו‍ֹנָהּ  because her sin is atoned for. Here the כִּי is causal, answering the question, "Why is her service finished?" The sin expressed by עָו‍ֹן is intentional sin; transgression and its guilt. This intentional sin is even paid for, or as the prophet says here, atoned (נִרְצָה, nifal perfect 3 m sg) for. The nifal voice reminds us that we are completely passive in the atonement for our sins; its action rest in God alone.

כִּי לָקְחָה מִיַּד יְהוָה כִּפְלַיִם בְּכָל-חַטֹּאתֶיהָ  For she has received from the hand of the LORD a double amount for all her sins. "She has received" (לָקְחָה) is a qal perfect, 3 fem sg. Once again the כִּי is causal, expressing in parallel the reason that her warfare or service is completed. There is no math involved in כִּפְלַיִם "a double amount" (like Jerusalem, another dual form). The "double" idea doesn't have to be pressed into a literalistic meaning: There is no end to God's forgiveness. ("Seven times, Lord?" "No, Peter. Seventy-seven times!"). Here the "sins" are the חַטָּאָה that signifies any sin or mistake at all. Christ completed the payment for every one of our sins (even double!); there is no more payment to be made. Anyone who looks as Christ and finds him lacking has an impossible task: to make up what he thinks Christ couldn't do. This is the dangerous quagmire of illogic that killed Judas Iscariot; this is the "What have I done?!" trap that the devil hurls at us like a Major League pitcher firing a screwball at an 8-year old up to the plate for his first at-bat in T-ball.

The first follow-up to "Comfort my people" is the purest gospel itself: Their sins are atoned for. If we had no other message, this would be enough. This message alone brings us into the lap of God once again; it does away with all of our sins and makes us children of our heavenly Father. We have peace through the blood of Jesus Christ.